Research ArticleMagnetized Anisotropic Dark Energy Models inBarberrsquos Second Self-Creation Theory

D D Pawar1 and Y S Solanke2

1 School of Mathematical Sciences Swami Ramanand Teerth Marathwada University Vishnupuri Nanded 431 606 India2Mungsaji Maharaj Mahavidyalay Darwha Yavatmal India

Correspondence should be addressed to D D Pawar dypawaryahoocom

Received 2 April 2014 Revised 14 July 2014 Accepted 23 July 2014 Published 24 August 2014

Academic Editor George Siopsis

Copyright copy 2014 D D Pawar and Y S SolankeThis is an open access article distributed under theCreativeCommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly citedThe publication of this article was funded by SCOAP3

The present paper deals with Bianchi type IX cosmological model with magnetized anisotropic dark energy by using Barberrsquos self-creation theory The energy momentum tensor consists of anisotropic fluid with EoS parameter 120596 and a uniform magnetic fieldof energy density 120588

119861 In order to obtain the exact solution we have assumed that dark energy components and the components of

magnetic field interact minimally and obey the law of conservation of energymomentum tensorsWe have also used the special lawof variation for the mean generalized Hubble parameter and power law relation between scalar field and scale factor Some physicaland kinematical properties of the models have been discussed

1 Introduction

In an attempt to produce continuous creation theories in1982 Barber [1] has proposed two self-creation theoriesmodifying the Brans and Dicke [2] and Brans [3] theoryof gravitation and Einstein theory of general relativity In1987 Brans has pointed out that the first theory of Bar-ber is not satisfactory because of violation of equivalenceprinciple According to Brans Barberrsquos first theory is notin disagreement with experimental observations and is alsonot consistent in general His second self-creation theory isa modification of Einsteinrsquos general theory of gravitation tovariable G-theory which predicts local effect and is withinthe observational limit In his postulate the gravitationalcoupling of the Einstein field equations is allowed to be avariable scalar on the space time so that this scalar couplesto the trace of energy momentum tensors Hence the fieldequations in Barberrsquos second self-creation theory are

(i) 119877119894119895 =1

2

119892119894119895119877 = minus

8120587

120593

119879119894119895

(ii) ◻120593 = 8

3

120587120582119879

(1)

Pimental [4] Sing and Deo [5] Soleng [6 7] Reddy [8 9]Maharaj and Beesham [10] Venkateswaru and Reddy [11 12]

Shanti and Rao [13] Mohanti and Pradhan [14] and Pawaret al [15 16] are some of the authors who have investigatedthe various aspects of Barberrsquos second self-creation theoryby using various cosmological models As we are unknownabout the dark energy but it is necessary to explain Therecent observations from high red shift type Ia supernovaeindicate the accelerated expansion of the universe which isconfirmed by the combinations of the results from the largescale distribution of galaxies and the remarkable data oncosmic microwave background (CMB) According to Riess etal [17 18] Permutter et al [19ndash21] and Spergel et al [22 23]all these observational results strongly imply the existenceof extra components with negative pressure Thus all theseobservational results are supporting the fact that universeis accelerating According to Caldwell et al [24 25] theseobservational findings also suggest that there should be atransition of the universe from the earlier deceleration phaseto the recent accelerating phase Even though at presentrecent observations supported that the universe is accelerat-ing but according to physicists there is no guarantee that itwill do so forever Moreover some of the physicists come tothe decision that the present acceleration of the universe maybe followed by deceleration even though universe may haveoscillatorymode of expansion In order to explain the cosmic

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2014 Article ID 859638 9 pageshttpdxdoiorg1011552014859638

2 Advances in High Energy Physics

acceleration of the universe the cosmologists have proposedmany candidates The cosmological constant is one of themost obvious theoretical candidates for dark energy despitehaving two limitations namely fine tuning and cosmiccoincidence problems Cohen et al [26] Copeland et al [27]and Deo et al [28] In addition to the cosmological constantan alternative proposal for dark energy is dynamical darkenergy scenario The quintessence phantom field Caldwell[24] Ratra and Peebles [29] quintom Elizalde et al [30]Chaplygin gas models Kamenshchik et al [31] tachyon fieldPadmanabhan [32] holographic Setare [33] are some ofthe examples of dark energy models Recently Pawar etal [34 35] studied Kantowski-Sachs cosmological modelswith constant EoS parameter in Barberrsquos second self-creationtheory and dark energy models in Brans-Dicke theory ofgravitation

An anisotropic cosmological model plays an importantrole in the large scale behavior of the universe Manyresearchers working on cosmology by using relativistic cos-mological models have not given proper reasons to believein a regular expansion for the description of the early stagesof the universe Anisotropies in the CMB are related tosmall perturbation superimposed on the perfectly smoothbackground which are believed to seed formation of galaxiesand large scale structure in the universe There are someexperimental data of CMR and theoretical arguments whichsupport the existence of anisotropic universe (Chimento [36]Misner [37] Land and Maqueijo [38] Demianski [39] andPawar et al [40 41])

In the present paper we have used magnetic anisotropicBianchi type IX space time Many researchers are usingBianchi type IX space time because this space time modelallows not only expansion but also rotation and shear Baliand Dave [42] have investigated this model in general theoryof relativity Tyagi and Sharma [43] have used this modelfor perfect fluid distribution in general relativity Rao andSanyasiraju [44 45] have studied Bianchi types VIII and IXmodels in zeromass scalar fields and self-creation cosmologyPawar and Dagwal [46] investigated Bianchi type IX twofluids cosmological models in general relativity Most of themodels have been studied by considering perfect fluid but itis not sufficient to describe the dynamics of an acceleratinguniverse This motivates the researchers to consider themodels of the universe filled with DE and magnetic fieldIn the present paper we have investigated Bianchi typeIX magnetized anisotropic space time Barberrsquos second self-creation theory We have obtained the exact solution of thefield equations The physical and geometrical properties ofthe models are discussed

2 Metric and Field Equations

We consider Bianchi type IX metric in the form

1198891199042= minus119889119905

2+ 1198862(119905) 119889119909

2+ 1198872(119905) 119889119910

2

+ (1198872sin2119910 + 1198862cos2119910) 1198891199112 minus 21198862 cos119910119889119909119889119911

(2)

where 119886 and 119887 are the functions of cosmic time 119905

The field equations in Baberrsquos second self-creation theoryare

119866119894119895= 119877119894119895minus

1

2

119892119894119895119877 =

minus8120587

120593

119879119894119895 (3)

◻120593 = 120593119896

119896=

8

3

120587120582119879 (4)

where 120582 is coupling constant and 120593 is Barberrsquos scalarWe consider the energy momentum tensor for the mag-

netized anisotropic DE fluid

119879119895

119894= dia [1198791

1 1198792

2 1198793

3 1198794

4]

= dia [minus119901119909+ 120588119861 minus119901119910minus 120588119861 119901119911minus 120588119861 120588 + 120588

119861]

= dia [minus120596119909120588 + 120588119861 minus120596119910120588 minus 120588119861 minus120596119911120588 minus 120588119861 120588 + 120588

119861]

= dia [minus (120596 + 120575) 120588 + 120588119861 minus (120596 + 120574) 120588 minus 120588119861

minus (120596 + 120574) 120588 minus 120588119861 (120588 + 120588

119861)]

(5)

where 120596119909

= 120596 + 120575 120596119910

= 120596 + 120574 and 120596119911= 120596 + 120574

are the directional EoS parameters on 119883- 119884- and 119885-axesrespectively 120588 is the energy density of the dark energy and120588119861is the energy density of the magnetic fieldIn a comoving coordinate system Einsteinrsquos field (3) with

(4) and (5) for the Bianchi type IX space time metric (2)subsequently leads to the following system of equations

2119887

119887

+

1198872

1198872+

1

1198872minus

3

4

1198862

1198874= minus

8120587

120593

[minus (120596 + 120575) 120588 + 120588119861]

119886

119886

+

119887

119887

+

119886

119886

119887

119887

+

1198862

41198874= minus

8120587

120593

[minus (120596 + 120574) 120588 minus 120588119861]

119886

119886

+

119887

119887

+

119886119887

119886119887

+

1198862

41198874= minus

8120587

120593

[minus (120596 + 120574) 120588 minus 120588119861]

2 119886119887

119886119887

+

1198872

1198872minus

1

4

1198862

1198874+

1

1198872= minus

8120587

120593

[(120588 + 120588119861)]

minus

120593 minus(

119886

119886

+ 2

119887

119887

) =

8

3

120587120582 (1 minus 120575 minus 2120574 minus 3120596) 120588

(6)

Thus the above system of the equations reduces and takes theform

2

119887

119887

+

1198872

1198872+

1

1198872minus

3

4

1198862

1198874= minus

8120587

120593

[minus (120596 + 120575) 120588 + 120588119861] (7)

119886

119886

+

119887

119887

+

119886119887

119886119887

+

1198862

41198874= minus

8120587

120593

[minus (120596 + 120574) 120588 minus 120588119861] (8)

2 119886119887

119886119887

+

1198872

1198872minus

1

4

1198862

1198874+

1

1198872= minus

8120587

120593

[(120588 + 120588119861)] (9)

minus

120593 minus(

119886

119886

+ 2

119887

119887

) =

8

3

120587120582 (1 minus 120575 minus 2120574 minus 3120596) 120588 (10)

Advances in High Energy Physics 3

By the law of conservation we have the Bianchi identity

120588 + (

119886

119886

+

2119887

119887

) (1 + 120596) 120588 + (

119886

119886

120575 +

2119887

119887

120574)120588

+ (120588119861+

4119887

119887

120588119861) = 0

(11)

Here we assume that DE components and magnetic fieldinteract minimally

3 Solutions of the Field Equations

The above system of the equations (7) to (11) containing eightunknown variables 119886 119887 120588 120588

119861 120596 120574 120575 and 120593 in five linearly

independent equations The first three variables are Einsteinfield equations whereas the fourth and fifth variables are Bar-berrsquos scalar field equation and Bianchi identity respectivelyIn order to solve this undetermined system three additionalconstraints are required

As the DE component and magnetic field interact mini-mally the Bianchi identity given by (11) can be split up intotwo separately additive conserved components namely theenergy momentum tensors for the dark energy and energymomentum tensor for the magnetic field

119866120592

120583120592= 119879120592

120583120592+ 119879(120573)120592

120583120592= 0 (12)

Thus the conservations of the energy momentum of theDE are given by

119879120592

120583120592= 120588 + (1 + 120596) 120588(

119886

119886

+

2119887

119887

) + 120588(

119886

119886

120575 +

2119887

119887

120574) = 0 (13)

And the conservation of the energy momentum tensor ofthe magnetic field is given by

119879(119861)120592

120583120592= 120588119861+

4119887

119887

120588119861= 0 (14)

After integration (14)rArr

120588119861=

1198961

1198874 (15)

where 1198961is the constant of integration But conservation

of the energy momentum of the dark energy can also bedecomposed into two parts

119879120592

120583120592= 1198791015840120592

120583120592+ 120591120592

120583120592= 0 (16)

The last term in (13) is 120591120592120583120592

which arises due to deviationfrom EoS parameter 120596 whereas the first two terms of (13) are1198791015840120592

120583120592which arise due to no deviation But according to our

assumption (Akarsu and Kilinc [47]) we have

1198791015840120592

120583120592= 120588 + (1 + 120596) 120588(

119886

119886

+

2119887

119887

) = 0 (17)

120591120592

120583120592= 120588(

119886

119886

120575 +

2119887

119887

120574) = 0 (18)

According to (17) and (18) the behavior of the energydensity of the DE component is controlled by the deviationfree part 1198791015840 of the EoS parameter 120596 of the DE but thisdeviation does not affect energy density of the DE directly Itaffects EoS parameter 120596 The choice of skewness parameters(120575 120574) is arbitrary it may be constant or itmay be the functionof cosmic time But since we are interested in physicallyvariable models of the universe consistent with observationsthe skewness parameters 120575 and 120574 are assumed to be thefunctions of cosmic time Here the skewness parameters 120575and 120574 are assumed to be a special dynamics on 119909 119910 and119911 axes consistent with (18) The dynamics of the skewnessparameters 120575(119905) on the 119909-axis is assumed to be (by Akarsuand Kilinc)

120575 (119905) = 119873

2

3

119887

119887

(

119886

119886

+

2119887

119887

)

1

120588(119889119890)

(19)

The dynamics of the skewness parameter 120574(119905) on 119910- and 119911-axes is given by

120574 (119905) = minus119873

1

3

119886

119886

(

119886

119886

+

2119887

119887

)

1

120588(119889119890)

(20)

As per our assumption (Berman [48]) the variations ofmean generalized Hubblersquos parameter for the Bianchi type IXmetric may be given by

119867 = 119897(1198861198872)

minus1198993

(21)

where 119897 gt 0 and 119899 ge 0 are constants The spatial volume 119881 isgiven by

119881 = 1198773= 1198861198872 (22)

where 119877 is average mean scalar factor The mean generalizedHubble parameter 119867 for the Bianchi type IX metric may begiven by

119867 =

119877

=

1

3

119881

=

1

3

(1198671+ 1198672+ 1198673)

=

1

3

(

119886

119886

+

119887

119887

+

119887

119887

) =

1

3

(

119886

119886

+

2119887

119887

)

(23)

where1198671and119867

2= 1198673are the directionalHubble parameters

along 119909- and 119910 = 119911-axes respectively They are defined by

1198671= 119867119909=

119886

119886

1198672= 119867119910=

119887

119887

(119867119910= 119867119911) (24)

On integration equating (21) and (23) yields

119877 = (119899119897119905 + 1198881)1119899 119899 = 0 (25)

119877 = 1198882119890119897119905 119899 = 0 (26)

Thus (21) gives two cosmological models of the universedepending on the values of 119899 When 119899 = 0 we aregetting power expansion model and when 119899 = 0 we are

4 Advances in High Energy Physics

getting exponential expansion model Further in view of theanisotropy of the space time in order to obtain determinatesolution we have to assume two more constraints as

119886 = 119877119898 (27)

where 119898 is constant and the power law relation betweenaverage scale factor119877 and the scalar field120593 (Johri andDesikan[49]) yields

120593 prop 119877119871997904rArr 120593 = 119888119877

119871 (28)

where 119871 is any integer and 119888 is the constant of proportionality

31 Power ExpansionModelWhen 119899 = 0 Average scale factorfor this model by (25) is

119877 = (119899119897119905 + 1198881)1119899 (29)

Hence the scalar field 120593 from (25) and (28) is

120593 = 119888(119899119897119905 + 1198881)119871119899 (30)

Equations (25) and (27) give

119886 = (119899119897119905 + 1198881)119898119899 (31)

From (22) (25) and (31) we have

119887 = (119899119897119905 + 1198881)(3minus119898)2119899

(32)

Equations (22) and (25) give the spatial volume as

119881 = (119899119897119905 + 1198881)3119899 (33)

The directional Hubble parameters defined by (24) take theform

1198671=

119897

(119899119897119905 + 1198881)

1198672= 1198673=

(3 minus 119898) 119897

2 (119899119897119905 + 1198881)

(34)

Hence the mean generalized Hubble parameter defined in(23) takes the form

119867 =

119897

(119899119897119905 + 1198881)

(35)

The expansion scalar 120579 mean anisotropy parameter 119860119898 and

shear scalar 120590 are respectively given by

120579 =

3119897

(119899119897119905 + 1198881)

(36)

119860119898=

(1198982minus 2119898 + 1)

2

(37)

1205902=

91198972

2(119899119897119905 + 1198881)2 (38)

Using (31) and (32) Bianchi type IX cosmologicalmodel in (2)in Barberrsquos second self-creation theory takes the form

1198891199042= minus119889119905

2+ (119899119897119905 + 119888

1)2119898119899

1198891199092+ (119899119897119905 + 119888

1)(3minus119898)119899

1198891199102

+ [(119899119897119905 + 1198881)(3minus119898)119899sin2119910 + (119899119897119905 + 119888

1)2119898119899cos2119910] 1198891199112

minus 2(119899119897119905 + 1198881)2119898119899 cos119910119889119909119889119911

(39)

Equations (15) and (31) give the energy density of magneticfield as

120588119861=

1198961

(119899119897119905 + 1198881)2(3minus119898)119899

(40)

Using (9) with (30) (31) (32) and (40) energy density of theDE is

120588 =

minus1198961

(119899119897119905 + 1198881)2(3minus119898)119899

minus

119888

8120587

3 (119898 + 1) (3 minus 119898) 1198972

4(119899119897119905 + 1198881)(2119899minus119871)119899

minus

1

4(119899119897119905 + 1198881)(2(3minus119898)minus119871)119899

+

1

(119899119897119905 + 1198881)(3minus119898minus119871)119899

(41)

Using (19) with (31) (32) and (41) skewness parameter 120575(119905)takes the form

120575 (119905) = (

32120587119873 (3 minus 119898) 1198972

(119899119897119905 + 1198881)119871119899

)

times [minus321205871198961(119899119897119905 + 119888

1)(2(119898+119899minus3)minus119871)119899

minus (9 + 6119898 minus 31198982) 1198881198972+ 119888(119899119897119905 + 119888

1)2(2119898+119899minus3)119899

minus 4119888(119899119897119905 + 1198881)[2119899minus(3minus119898minus2119871)]119899

]

minus1

(42)

Using (20) with (31) (32) and (41) the skewness parameter120574(119905) takes the form

120574 (119905) = (

minus321205871198731198981198972

(119899119897119905 + 1198881)119871119899)

times [minus321205871198961(119899119897119905 + 119888

1)(2(119898+119899minus3)minus119871)119899

minus (9 + 6119898 minus 31198982) 1198881198972+ 119888(119899119897119905 + 119888

1)2(2119898+119899minus3)119899

minus 4119888(119899119897119905 + 1198881)[2119899minus(3minus119898minus2119871)]119899

]

minus1

(43)

Advances in High Energy Physics 5

Using (17) with (31) (32) and (41) the EoS parameter of themodel is

120596 (119905) = (2119898 minus 3) 1198961119897(119899119897119905 + 119888

1)(2119898minus119899minus6)119899

+

119888

8120587

[

1198973(119898 + 1) (3 minus 119898) (9 + 3119871 minus 6119899)

4

times (119899119897119905 + 1198881)(119871minus3119899)119899

]

+

119888

8120587

[minus

(119871 + 2119898 minus 3) 119897

4

(119899119897119905 + 1198881)(2119898+119871minus119899minus6)119899

+ (119871 + 119898) 119897(119899119897119905 + 1198881)(119871+119898minus3minus119899)

]

(44)

311 Physical Behavior of the Model When 119899 = 0 In thismodel the direction the directional Hubble parameter meangeneralized Hubble parameters expansion scalar Barberrsquosscalar field and shear scalar all are the functions of the cosmictime except themean anisotropy parameter119860

119898 It is constant

throughout the universe All the above parameters vanishwhen cosmic time is infinite whereas these parametersare finite when time is zero except the directional Hubbleparameter119867

2 It follows the above property provided119898 = 3

The spatial volume of this model is also a function of cosmictime and it increases with increase in timeThat is the modelis expanding with time The energy density of the model isconstant when cosmic time zero 119898 = 3 but when 119898 = 3

the energy density of the magnetic field is 1198961and it vanishes

when 119905 is infinite The energy density of the DE is constantwhen cosmic time is zero and it tends to zero when cosmictime tends to infinite when119898 = 3 but when119898 = 3 (119871 119899 gt 0)the energy density of the DE is minus119896

1+ (311988832120587)(119899119897119905 + 119888

1)119871119899

Thus in this case the energy density of DE increases withincrease in cosmic time and when 119905 = 0 energy density ofDE is minus119896

1+ (311988832120587)119888

119871119899

1= constant Similarly the skewness

parameters 120575(119905) 120574(119905) as well as EoS parameter 120596(119905) are thefunctions of cosmic time 119905 Also lim

119905rarrinfin(120590120579)2

= 0 Hencethis model does not approach the isotropy

We now extend our work to investigate the consistency ofmodel (39) with the observational parameters from the pointof astrophysical phenomena

(1) Look-Back Time RedshiftThe look-back time 119905119871is defined

as the difference between the present age of the universe 1199050

and the age of the universe 119905 when a particular light ray atredshift 119911 was emitted

The average scale factor of the universe 119877 for a givenredshift 119911 is related to the present scale factor 119877

0by the

relation 1 + 119911 = 1198770119877

Equations (25) and (35) give

1198670(1199050minus 119905) =

1

119899

[1 minus (1 + 119911)minus119899] (45)

After little manipulation we get

1198670(1199050minus 119905) = 119911 minus

(119899 minus 1)

2

1199112+ sdot sdot sdot (46)

Taking limit 119911 rarr infin in (45) the present age of the universeis

1198670(1199050minus 119905) =

1

119899

[1 minus 0] 997904rArr 1199050=

1

1198991198670

=

119867minus1

0

119899

119899 = 0

(47)

where1198670is the present value of the Hubble parameter

(2) Luminosity Distance RedshiftThe luminosity distance 119889119871

of a light source is defined as

119889119871= 11987701199031 (119911) (1 + 119911) (48)

where the radial coordinate distance 1199031(119911) of the object at light

emission is

1199031 (119911) = int

1199050

1199051

119889119905

119877

=

119867minus1

0119877minus1

0

(119899 minus 1)

[1 minus (1 + 119911)1minus119899] (49)

Solving (48) and (49) we get

1198670119889119871=

(1 + 119911)

(119899 minus 1)

[1 minus (1 + 119911)(1minus119899)

] (50)

32 Exponential ExpansionModelWhen 119899 = 0 Average scalefactor for this model by (26) is

119877 = 1198882119890119897119905 (51)

Thus from (26) and (28) we have the scalar field as

120593 = 119888119888119871

2119890(119871119897119905)

(52)

Equations (26) and (27)rArr

119886 = 119888119898

2119890(119898119897119905)

(53)

Similarly (22) (26) and (53)rArr

119887 = 119888(3minus119898)2

2119890((3minus119898)2)119897119905

119898 = 3 (54)

From (22) and (26) the spatial volume of this model is

119881 = 1198883

2119890(3119897119905)

(55)

The directional Hubble parameters1198671 1198672= 1198673are given by

1198671= 119898119897 (56)

1198672= 1198673=

(3 minus 119898) 119897

2

(57)

Thus the mean generalized parameters defined in (23) takethe form

119867 = 119897 = constant (58)

In this case expansion scalar 120579 mean anisotropy parameter119860119898 and shear scalar are respectively given by

120579 = 3119897

119860119898=

1

2

(1198982minus 2119898 + 1)

1205902=

91198972

2

(59)

6 Advances in High Energy Physics

Using (53) and (54) Bianchi type IX cosmological model in(2) in Barberrsquos second self-creation theory takes the form

1198891199042= minus119889119905

2+ 1198882119898

2119890(2119898119897119905)

1198891199092+ 119888(3minus119898)

2119890(3minus119898)119897119905

1198891199102

+ [119888(3minus119898)

2119890(3minus119898)119897119905sin2119910 + 1198882119898

2119890(2119898119897119905)cos2119910] 1198891199112

minus 21198882119898

2119890(2119898119897119905) cos119910119889119909119889119911

(60)

In this case (15) and (54) give the energy density of themagnetic field

120588119861=

1198961

1198882(3minus119898)

21198902(3minus119898)119897119905

(61)

Using (9) with (52) (53) (54) and (61) gives the energydensity of the DE

120588 = minus

1198961

1198882(3minus119898)

2

119890minus2(3minus119898)119897119905

minus

119888119888119871

2

8120587

(9 + 6119898 minus 3119898)21198972119890(119871119897119905)

4

minus

119888(4119898minus6)

2

4

119890(4119898+119871minus6)119897119905

+ 119888(119898minus3)

2119890(119871+119898minus3)119897119905

(62)

Equation (19) with (53) (54) and (62) gives the skewnessparameter 120575(119905) as

120575 (119905) = (32120587119873 (3 minus 119898) 1198972)

times (minus321205871198961[1198882119890minus119897119905]

2(3minus119898)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+ 119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119862[1198882119890119897119905]

(119871+119898minus3)

)

minus1

(63)

and similarly (20) with (53) (54) and (62) gives the skewnessparameter 120574(119905)

120574 (119905) = (minus321205871198731198981198972)

times minus321205871198961[1198882119890119897119905]

2(119898minus3)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119888[1198882119890119897119905]

(119898+119871minus3)

minus1

(64)

Equation (17) with (53) (54) and (62) gives the EoS parame-ter 120596(119905) as

120596 (119905) = (2119898 minus 3) 1198961119897[1198882119890119897119905]

2(119898minus3)

+

119888119888119871

2

8120587

[

(3 + 119871) 1198973(9 + 6119898 minus 3119898

2) 119890(119871119897119905)

4

minus

(4119898 + 119871 minus 3) 1198971198882(2119898minus3)

2119890(4119898+119871minus6)119897119905

4

+ (119871 + 119898) 119897119888(119898minus3)

2119890(119871+119898minus3)119897119905

]

(65)

321 The Physical Behavior of the Model When 119899=0 For thismodel average scale factor 119877 = 119888

2119890119897119905 and the scalar field

120593 = 119888119888119871

2119890119871119897119905 This model is nonsingular since the exponential

function never vanishes Thus this model does not have anyphysical singularity For this model the directional Hubbleparameters as well as mean generalized Hubble parameter119867are constant throughout the evolution of the universe Hence119889119867119889119905 = 0 This implies that the greater the value of Hubbleparameter the faster the rate of expansion of the universeHence this model may represent inflationary era in the earlystages of the universe and the very late time of the universeThe spatial volume of the universe is finite when cosmic timeis zero and expands exponentially as 119905 increases and becomesinfinite when 119905 = infin which indicates that universe startsits expansion with zero volume from finite past In this casethe expansion scalar 120579 and the mean anisotropy parameter119860119898are constants throughout the evolution of the universe

but mean anisotropy parameter is exactly the same as thepreviousmodelThe energy density of themagnetic field is 120588

119861

= 11989611198882(3minus119898)

2= constant when time 119905 = 0 and119898 = 3 but when

119898 = 3 it is equal to constant 1198961 The density of the magnetic

field vanisheswhen the cosmic time is infinite Energy densityof theDE is some finite number when cosmic time is zero andit increases with increase in time and it becomes infinite whentime is infinite The skewness parameters 120575(119905) 120574(119905) as well asEoS parameters 120596(119905) are the functions of cosmic time 119905 Inthis model also lim

119905rarrinfin(120590120579)2

= 0 Hence this model doesnot approach the isotropy

In this case also we extend our work to investigate theconsistency of model (57) with the observational parametersfrom the point of astrophysical phenomena

(1) Look-Back Time Redshift From (26) and (53) we have

119867(1199050minus 119905) = log (1 + 119911) (66)

Thus for small 119911 we have

1198670(1199050minus 119905) = log (1 + 119911) = [119911 minus 119911

2

2

+ sdot sdot sdot ]

where 119905 = 1199050minus

log (1 + 119911)119867

(67)

Advances in High Energy Physics 7

(2) Luminosity Distance Redshift The luminosity distance oflight source is given by

1198670119889119871= 119911 (1 + 119911) 997904rArr 119889

119871=

119911 (1 + 119911)

119867

(68)

The above equation shows that the luminosity distanceincreases faster with the redshift when 119899 = 0

4 Conclusion

In the present paper we have discussed magnetized Bianchitype IX cosmological model in Barberrsquos second self-creationtheory We have studied the minimal interaction betweenmagnetic field and DE which will help us in detecting DEWe have obtained the exact solution of the Bianchi type IXcosmological model It is observed that in both models EoSparameter is a function of cosmic time which supportedthe recent observations The interesting and remarkableobservation of the present paper is that the mean anisotropyparameter 119860

119898for both models is the same and is constant

Also lim119905rarrinfin

(120590120579)2= 0 for bothmodels Hence bothmodels

do not approach the isotropyWe have also studied the two astrophysical phenomena

such as look-back time redshift and luminosity distanceredshift for both models and observed that such models arecompatible with recent observations because from the pointof recent astronomical measurements obtained by Pawaret al [15 16] Riess et al [17 18] and Permutter et al[19] the SN (supernovae) Hubble diagram derived from theobservations of hundreds of SNe detected over the borderrange of redshifts has amply demonstrated that the universeis expanding with acceleration Further confirmation for theaccelerating universe came from the recent observations of Iatype of SNe studied by Pawar et al [16] Tonry et al [50] andClocchiatti et al [51] Within the general relativity in orderto explain the accelerated expansion of the universe a nearlysmooth formof energy of large negative pressure is inevitableConfirmation by Bennett et al [52] regarding the filling-in ofthe universe by a dominated component of energy with largenegative pressure dubbed as dark energy was provided bythe measurements of cosmic microwave background (CMB)and large scale structure (LSS) studied by Tegmark et al [53]This formof energy is believed to account for about 75of theuniverseThe current observational data obtained by Friemanet al [54] provide strong evidence regarding the existence ofdark energy and further demonstrate that the fractional ofcritical that is being contributed by the dark energy may goas high as 076pm002

Our present model is noninteracting Bianchi type IXcosmological model which cannot resolve the coincidenceproblem since it predicts inclusive system in which magneticenergy density decreases faster (which is inversely propor-tional to scale factor) while density of the dark energy eitherremains constant or increasesThe interactingmodels play animportant role in the study of coincidence problem [55 56]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like thank the referee for invaluablesuggestions

References

[1] G A Barber ldquoOn two ldquoself-creationrdquo cosmologiesrdquo GeneralRelativity and Gravitation vol 14 no 2 pp 117ndash136 1982

[2] C Brans and R H Dicke ldquoMachrsquos principle and a relativistictheory of gravitationrdquo Physical Review vol 124 no 3 pp 925ndash935 1961

[3] C H Brans ldquoConsistency of field equations in ldquoself-creationrdquocosmologiesrdquo General Relativity and Gravitation vol 19 no 9pp 949ndash952 1987

[4] L O Pinental ldquoExact self-creation cosmological solutionsrdquoAstrophysics and Space Science vol 116 pp 395ndash399 1985

[5] R T Sing and S Deo ldquoZero-mass scalar interactions in theRobertson-Walker Universerdquo Acta Physica Hungarica vol 59no 3-4 pp 321ndash325 1986

[6] H H Soleng ldquoCosmic shear in inflationary models of Bianchitypes VIII and IXrdquo Astrophysics and Space Science vol 137 pp373ndash384 1987

[7] H H Soleng ldquoSelf-creation cosmological solutionsrdquo Astro-physics and Space Science vol 139 no 1 pp 13ndash19 1987

[8] D R K Reddy ldquoBianchi type-I vacuum model in self-creationcosmologyrdquo Astrophysics and Space Science vol 132 no 2 pp401ndash403 1987

[9] D R K Reddy ldquoVacuum friedmann model in self-creationcosmologyrdquo Astrophysics and Space Science vol 133 no 1 pp189ndash191 1987

[10] S D Maharaj and A Beesham ldquoOpen and closed Robertson-Walker-type Lyttleton-Bondi universesrdquo Astrophysics and SpaceScience vol 140 no 1 pp 33ndash37 1988

[11] R Venkateswaru and D R K Reddy ldquoBianchi type-V radiatingmodel in self creation cosmologyrdquo Astrophysics and SpaceScience vol 151 p 353 1989

[12] R Venkateswaru and D R K Reddy Astrophysics and SpaceScience 152337 1989

[13] K Shanti and V U M Rao ldquoBianchi type-II and III modelsin self-creation cosmologyrdquo Astrophysics and Space Science vol179 no 1 pp 147ndash153 1991

[14] G Mohanti and B D Pradhan ldquoCosmological mesonic viscousfluid modelrdquo International Journal of Theoretical Physics vol 1article 31 1992

[15] D D Pawar S N Bayaskar and V R Patil ldquoPlane symmetriccosmological model with thick domain walls in Brans-Dicketheory of gravitationrdquo Bulgarian Journal of Physics vol 36 pp68ndash75 2009

[16] D D Pawar S N Bayaskar and A G Deshmukh ldquoStringcosmological model in presence of massless scalar field inmodified theory of general relativityrdquo Romanian Reports ofPhysics vol 56 no 5-6 pp 842ndash848 2011

[17] A G Riess A V Filippenko P Challis et al ldquoObservationalevidence from supernovae for an accelerating universe and

8 Advances in High Energy Physics

a cosmological constantrdquo The Astronomical Journal vol 116article 1009 1998

[18] A G Riess L-G Strolger J Tonry et al ldquoType Ia supernovadiscoveries at 119911 gt 1 from the Hubble Space Telescope evidencefor past deceleration and constraints on dark energy evolutionrdquoThe Astrophysical Journal vol 607 pp 665ndash687 2004

[19] S Permutter S Gabi G Goldhaber et al ldquoMeasurements ofthe cosmological parameters omega and lambda from the first7 supernovae at 119911 ge 035rdquoThe Astrophysical Journal vol 483 p565 1997

[20] S J Permutter G Aldering M Della Valle et al ldquoDiscovery ofa supernova explosion at half the age of the Universerdquo Naturevol 391 pp 51ndash54 1998

[21] S J Permutter G Aldering G Goldhaber et al ldquoMeasurementsofΩ and Λ from 42 High-Redshift SupernovaerdquoThe Astrophys-ical Journal vol 517 no 2 p 565 1999

[22] D N Spergel L Verde H V Peiris et al ldquoFirst-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations determi-nation of cosmological parametersrdquo The Astrophysical JournalSupplement Series vol 148 no 1 p 175 2003

[23] D N Spergel R Bean O Dore et al ldquoThree-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations implica-tions for cosmologyrdquo The Astrophysical Journal SupplementSeries vol 170 no 2 article 377 2007

[24] R RCaldwell ldquoCosmicMicrowaveBackground and Supernovaconstraints on quintessence concordance regions and targetmodelsrdquo Physical Review D vol 69 2004

[25] R R Caldwell ldquoSudden gravitational transitionrdquo PhysicalReview D vol 73 2006

[26] A G Cohen D B Kaplan and A E Nelson ldquoEffective fieldtheory black holes and the cosmological constantrdquo PhysicalReview Letters vol 82 no 25 pp 4971ndash4974 1999

[27] E J Copeland M Sami and S Tsujikawa ldquoDynamics of darkenergyrdquo International Journal of Modern Physics vol 15 no 11pp 1753ndash1935 2006

[28] A Deo J S Alcaniz and D Jain ldquoCosmological consequencesof a chaplygin gas dark energyrdquo Physical Review D vol 67Article ID 023515 2004

[29] B Ratra and J Peebles ldquoFractal model for disordered magnetsrdquoPhysical Review D vol 37 p 321 1988

[30] R R Caldwell ldquoA phantom menace Cosmological conse-quences of a dark energy component with super-negativeequation of staterdquo Physics Letters B vol 545 no 1-2 pp 23ndash292002

[31] E Elizalde S Nojiri and S D Odinstov ldquoLate-time cosmologyin a (phantom) scalar-tensor theory dark energy and thecosmic speed-uprdquo Physical Review D vol 70 no 4 Article ID043539 2004

[32] A Kamenshchik U Moschella and V Pasquier ldquoAn alternativeto quintessencerdquo Physics Letters B vol 511 no 2-4 pp 265ndash2682001

[33] T Padmanabhan ldquoAccelerated expansion of the universe drivenby tachyonic matterrdquo Physical Review D vol 66 Article ID021301 2002

[34] D D Pawar Y S Solanke and S N Bayaskar ldquoKantowski-sachscosmological models with constat EoS parameter in BarberrsquosSecond Self Creation Theoryrdquo Prespacetime Journal vol 5 no2 pp 60ndash68 2014

[35] D D Pawar and Y S Solanke ldquoExact kantowski-sachsanisotropic dark energy cosmological models in brans dicke

theory of gravitationrdquo International Journal of TheoreticalPhysics vol 53 no 9 pp 3052ndash3065 2014

[36] L P Chimento ldquoExtended tachyon field Chaplygin gas andsolvable 119896-essence cosmologiesrdquo Physical Review D vol 69 no12 Article ID 123517 10 pages 2004

[37] C W Misner ldquoThe isotropy of the universerdquo The AstrophysicalJournal vol 151 p 431 1968

[38] K Land and J Maqueijo ldquoExamination of evidence for apreferred axis in the cosmic radiation anisotropyrdquo PhysicalReview Letters vol 95 Article ID 071301 2005

[39] M Demianski ldquoTilted plane symmetric magnetized cosmolog-ical modelsrdquo Physical Review D vol 46 no 4 pp 1391ndash13981992

[40] D D Pawar V D Dagwal and Y S Solanke ldquoTilted plane sym-metricmagnetized cosmological modelsrdquo Prespacetime Journalvol 5 no 2 pp 368ndash377 2014

[41] D D Pawar and V J Dagwal ldquoBianchi type IX string cos-mological model in general relativityrdquo International Journal ofTheoretical Physics vol 53 no 7 pp 2441ndash2450 2014

[42] R Bali and S Dave ldquoBianchi type IX string cosmological modelfor perfect fluid distribution in general relativityrdquo PramanaJournal of Physics vol 56 p 4 2001

[43] A Tyagi and K Sharma ldquoBianchi type IX string cosmologicalmodel for perfect fluid distribution in general relativityrdquoChinesePhysics Letters vol 27 no 7 Article ID 079801 2010

[44] V U M Rao and Y V S S Sanyasiraju ldquoExact Bianchi-typeVIII and IX models in the presence of zero-mass scalar fieldsrdquoAstrophysics and Space Science vol 187 no 1 pp 113ndash117 1992

[45] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 no 4 pp 689ndash6932013

[46] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 pp 689ndash693 2013

[47] O Akarsu and C B Kilinc ldquoLRS Bianchi type I models withanisotropic dark energy and constant deceleration parameterrdquoGeneral Relativity and Gravitation vol 42 pp 119ndash140 2010

[48] M S Berman ldquoA special law of variation for Hubblersquos parame-terrdquo Il Nuovo Cimento B vol 74 pp 182ndash186 1983

[49] V B Johri andK Desikan ldquoCosmological models with constantdeceleration parameter in Brans-Dicke theoryrdquoGeneral Relativ-ity and Gravitation vol 26 no 12 pp 1217ndash1232 1994

[50] J L Tonry B P Schmidt B Barris et al ldquoCosmological resultsfrom high-z supernovaerdquoThe Astrophysical Journal vol 594 p1 2003

[51] A Clocchiatti B P Schmidt and A V Filippenko ldquoHubbleSpace Telescope and Ground-based Observations of Type IaSupernovae at Redshift 05 Cosmological Implicationsrdquo TheAstrophysical Journal vol 642 no 1 2006

[52] C L Bennett R S Hill G Hinshaw et al ldquoFirst-yearWilkinson Microwave Anisotropy Probe (WMAP) observationsforeground emissionrdquo The Astrophysical Journal SupplementSeries vol 148 no 1 pp 97ndash117 2003

[53] M Tegmark M R Blanton M A Strauss et al ldquoThe three-dimensional power spectrum of galaxies from the sloan digitalsky surveyrdquoTheAstrophysical Journal vol 606 no 2 article 7022004

[54] J Frieman M Turner and D Huterer ldquoDark energy andthe accelerating universerdquo Annual Review of Astronomy andAstrophysics vol 46 pp 385ndash432 2008

Advances in High Energy Physics 9

[55] S del Campo C Fabris R Herrera and W Zimdahl ldquoHolo-graphic dark-energymodelsrdquo Physical Review D vol 83 ArticleID 123006 2011

[56] S del Campo R Herrera and D Pavon ldquoInteracting modelsmay be key to solve the cosmic coincidence problemrdquo Journalof Cosmology and Astroparticle Physics vol 2009 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

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Soft MatterJournal of

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AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

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Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in High Energy Physics 3

By the law of conservation we have the Bianchi identity

120588 + (

119886

119886

+

2119887

119887

) (1 + 120596) 120588 + (

119886

119886

120575 +

2119887

119887

120574)120588

+ (120588119861+

4119887

119887

120588119861) = 0

(11)

Here we assume that DE components and magnetic fieldinteract minimally

3 Solutions of the Field Equations

The above system of the equations (7) to (11) containing eightunknown variables 119886 119887 120588 120588

119861 120596 120574 120575 and 120593 in five linearly

independent equations The first three variables are Einsteinfield equations whereas the fourth and fifth variables are Bar-berrsquos scalar field equation and Bianchi identity respectivelyIn order to solve this undetermined system three additionalconstraints are required

As the DE component and magnetic field interact mini-mally the Bianchi identity given by (11) can be split up intotwo separately additive conserved components namely theenergy momentum tensors for the dark energy and energymomentum tensor for the magnetic field

119866120592

120583120592= 119879120592

120583120592+ 119879(120573)120592

120583120592= 0 (12)

Thus the conservations of the energy momentum of theDE are given by

119879120592

120583120592= 120588 + (1 + 120596) 120588(

119886

119886

+

2119887

119887

) + 120588(

119886

119886

120575 +

2119887

119887

120574) = 0 (13)

And the conservation of the energy momentum tensor ofthe magnetic field is given by

119879(119861)120592

120583120592= 120588119861+

4119887

119887

120588119861= 0 (14)

After integration (14)rArr

120588119861=

1198961

1198874 (15)

where 1198961is the constant of integration But conservation

of the energy momentum of the dark energy can also bedecomposed into two parts

119879120592

120583120592= 1198791015840120592

120583120592+ 120591120592

120583120592= 0 (16)

The last term in (13) is 120591120592120583120592

which arises due to deviationfrom EoS parameter 120596 whereas the first two terms of (13) are1198791015840120592

120583120592which arise due to no deviation But according to our

assumption (Akarsu and Kilinc [47]) we have

1198791015840120592

120583120592= 120588 + (1 + 120596) 120588(

119886

119886

+

2119887

119887

) = 0 (17)

120591120592

120583120592= 120588(

119886

119886

120575 +

2119887

119887

120574) = 0 (18)

According to (17) and (18) the behavior of the energydensity of the DE component is controlled by the deviationfree part 1198791015840 of the EoS parameter 120596 of the DE but thisdeviation does not affect energy density of the DE directly Itaffects EoS parameter 120596 The choice of skewness parameters(120575 120574) is arbitrary it may be constant or itmay be the functionof cosmic time But since we are interested in physicallyvariable models of the universe consistent with observationsthe skewness parameters 120575 and 120574 are assumed to be thefunctions of cosmic time Here the skewness parameters 120575and 120574 are assumed to be a special dynamics on 119909 119910 and119911 axes consistent with (18) The dynamics of the skewnessparameters 120575(119905) on the 119909-axis is assumed to be (by Akarsuand Kilinc)

120575 (119905) = 119873

2

3

119887

119887

(

119886

119886

+

2119887

119887

)

1

120588(119889119890)

(19)

The dynamics of the skewness parameter 120574(119905) on 119910- and 119911-axes is given by

120574 (119905) = minus119873

1

3

119886

119886

(

119886

119886

+

2119887

119887

)

1

120588(119889119890)

(20)

As per our assumption (Berman [48]) the variations ofmean generalized Hubblersquos parameter for the Bianchi type IXmetric may be given by

119867 = 119897(1198861198872)

minus1198993

(21)

where 119897 gt 0 and 119899 ge 0 are constants The spatial volume 119881 isgiven by

119881 = 1198773= 1198861198872 (22)

where 119877 is average mean scalar factor The mean generalizedHubble parameter 119867 for the Bianchi type IX metric may begiven by

119867 =

119877

=

1

3

119881

=

1

3

(1198671+ 1198672+ 1198673)

=

1

3

(

119886

119886

+

119887

119887

+

119887

119887

) =

1

3

(

119886

119886

+

2119887

119887

)

(23)

where1198671and119867

2= 1198673are the directionalHubble parameters

along 119909- and 119910 = 119911-axes respectively They are defined by

1198671= 119867119909=

119886

119886

1198672= 119867119910=

119887

119887

(119867119910= 119867119911) (24)

On integration equating (21) and (23) yields

119877 = (119899119897119905 + 1198881)1119899 119899 = 0 (25)

119877 = 1198882119890119897119905 119899 = 0 (26)

Thus (21) gives two cosmological models of the universedepending on the values of 119899 When 119899 = 0 we aregetting power expansion model and when 119899 = 0 we are

4 Advances in High Energy Physics

getting exponential expansion model Further in view of theanisotropy of the space time in order to obtain determinatesolution we have to assume two more constraints as

119886 = 119877119898 (27)

where 119898 is constant and the power law relation betweenaverage scale factor119877 and the scalar field120593 (Johri andDesikan[49]) yields

120593 prop 119877119871997904rArr 120593 = 119888119877

119871 (28)

where 119871 is any integer and 119888 is the constant of proportionality

31 Power ExpansionModelWhen 119899 = 0 Average scale factorfor this model by (25) is

119877 = (119899119897119905 + 1198881)1119899 (29)

Hence the scalar field 120593 from (25) and (28) is

120593 = 119888(119899119897119905 + 1198881)119871119899 (30)

Equations (25) and (27) give

119886 = (119899119897119905 + 1198881)119898119899 (31)

From (22) (25) and (31) we have

119887 = (119899119897119905 + 1198881)(3minus119898)2119899

(32)

Equations (22) and (25) give the spatial volume as

119881 = (119899119897119905 + 1198881)3119899 (33)

The directional Hubble parameters defined by (24) take theform

1198671=

119897

(119899119897119905 + 1198881)

1198672= 1198673=

(3 minus 119898) 119897

2 (119899119897119905 + 1198881)

(34)

Hence the mean generalized Hubble parameter defined in(23) takes the form

119867 =

119897

(119899119897119905 + 1198881)

(35)

The expansion scalar 120579 mean anisotropy parameter 119860119898 and

shear scalar 120590 are respectively given by

120579 =

3119897

(119899119897119905 + 1198881)

(36)

119860119898=

(1198982minus 2119898 + 1)

2

(37)

1205902=

91198972

2(119899119897119905 + 1198881)2 (38)

Using (31) and (32) Bianchi type IX cosmologicalmodel in (2)in Barberrsquos second self-creation theory takes the form

1198891199042= minus119889119905

2+ (119899119897119905 + 119888

1)2119898119899

1198891199092+ (119899119897119905 + 119888

1)(3minus119898)119899

1198891199102

+ [(119899119897119905 + 1198881)(3minus119898)119899sin2119910 + (119899119897119905 + 119888

1)2119898119899cos2119910] 1198891199112

minus 2(119899119897119905 + 1198881)2119898119899 cos119910119889119909119889119911

(39)

Equations (15) and (31) give the energy density of magneticfield as

120588119861=

1198961

(119899119897119905 + 1198881)2(3minus119898)119899

(40)

Using (9) with (30) (31) (32) and (40) energy density of theDE is

120588 =

minus1198961

(119899119897119905 + 1198881)2(3minus119898)119899

minus

119888

8120587

3 (119898 + 1) (3 minus 119898) 1198972

4(119899119897119905 + 1198881)(2119899minus119871)119899

minus

1

4(119899119897119905 + 1198881)(2(3minus119898)minus119871)119899

+

1

(119899119897119905 + 1198881)(3minus119898minus119871)119899

(41)

Using (19) with (31) (32) and (41) skewness parameter 120575(119905)takes the form

120575 (119905) = (

32120587119873 (3 minus 119898) 1198972

(119899119897119905 + 1198881)119871119899

)

times [minus321205871198961(119899119897119905 + 119888

1)(2(119898+119899minus3)minus119871)119899

minus (9 + 6119898 minus 31198982) 1198881198972+ 119888(119899119897119905 + 119888

1)2(2119898+119899minus3)119899

minus 4119888(119899119897119905 + 1198881)[2119899minus(3minus119898minus2119871)]119899

]

minus1

(42)

Using (20) with (31) (32) and (41) the skewness parameter120574(119905) takes the form

120574 (119905) = (

minus321205871198731198981198972

(119899119897119905 + 1198881)119871119899)

times [minus321205871198961(119899119897119905 + 119888

1)(2(119898+119899minus3)minus119871)119899

minus (9 + 6119898 minus 31198982) 1198881198972+ 119888(119899119897119905 + 119888

1)2(2119898+119899minus3)119899

minus 4119888(119899119897119905 + 1198881)[2119899minus(3minus119898minus2119871)]119899

]

minus1

(43)

Advances in High Energy Physics 5

Using (17) with (31) (32) and (41) the EoS parameter of themodel is

120596 (119905) = (2119898 minus 3) 1198961119897(119899119897119905 + 119888

1)(2119898minus119899minus6)119899

+

119888

8120587

[

1198973(119898 + 1) (3 minus 119898) (9 + 3119871 minus 6119899)

4

times (119899119897119905 + 1198881)(119871minus3119899)119899

]

+

119888

8120587

[minus

(119871 + 2119898 minus 3) 119897

4

(119899119897119905 + 1198881)(2119898+119871minus119899minus6)119899

+ (119871 + 119898) 119897(119899119897119905 + 1198881)(119871+119898minus3minus119899)

]

(44)

311 Physical Behavior of the Model When 119899 = 0 In thismodel the direction the directional Hubble parameter meangeneralized Hubble parameters expansion scalar Barberrsquosscalar field and shear scalar all are the functions of the cosmictime except themean anisotropy parameter119860

119898 It is constant

throughout the universe All the above parameters vanishwhen cosmic time is infinite whereas these parametersare finite when time is zero except the directional Hubbleparameter119867

2 It follows the above property provided119898 = 3

The spatial volume of this model is also a function of cosmictime and it increases with increase in timeThat is the modelis expanding with time The energy density of the model isconstant when cosmic time zero 119898 = 3 but when 119898 = 3

the energy density of the magnetic field is 1198961and it vanishes

when 119905 is infinite The energy density of the DE is constantwhen cosmic time is zero and it tends to zero when cosmictime tends to infinite when119898 = 3 but when119898 = 3 (119871 119899 gt 0)the energy density of the DE is minus119896

1+ (311988832120587)(119899119897119905 + 119888

1)119871119899

Thus in this case the energy density of DE increases withincrease in cosmic time and when 119905 = 0 energy density ofDE is minus119896

1+ (311988832120587)119888

119871119899

1= constant Similarly the skewness

parameters 120575(119905) 120574(119905) as well as EoS parameter 120596(119905) are thefunctions of cosmic time 119905 Also lim

119905rarrinfin(120590120579)2

= 0 Hencethis model does not approach the isotropy

We now extend our work to investigate the consistency ofmodel (39) with the observational parameters from the pointof astrophysical phenomena

(1) Look-Back Time RedshiftThe look-back time 119905119871is defined

as the difference between the present age of the universe 1199050

and the age of the universe 119905 when a particular light ray atredshift 119911 was emitted

The average scale factor of the universe 119877 for a givenredshift 119911 is related to the present scale factor 119877

0by the

relation 1 + 119911 = 1198770119877

Equations (25) and (35) give

1198670(1199050minus 119905) =

1

119899

[1 minus (1 + 119911)minus119899] (45)

After little manipulation we get

1198670(1199050minus 119905) = 119911 minus

(119899 minus 1)

2

1199112+ sdot sdot sdot (46)

Taking limit 119911 rarr infin in (45) the present age of the universeis

1198670(1199050minus 119905) =

1

119899

[1 minus 0] 997904rArr 1199050=

1

1198991198670

=

119867minus1

0

119899

119899 = 0

(47)

where1198670is the present value of the Hubble parameter

(2) Luminosity Distance RedshiftThe luminosity distance 119889119871

of a light source is defined as

119889119871= 11987701199031 (119911) (1 + 119911) (48)

where the radial coordinate distance 1199031(119911) of the object at light

emission is

1199031 (119911) = int

1199050

1199051

119889119905

119877

=

119867minus1

0119877minus1

0

(119899 minus 1)

[1 minus (1 + 119911)1minus119899] (49)

Solving (48) and (49) we get

1198670119889119871=

(1 + 119911)

(119899 minus 1)

[1 minus (1 + 119911)(1minus119899)

] (50)

32 Exponential ExpansionModelWhen 119899 = 0 Average scalefactor for this model by (26) is

119877 = 1198882119890119897119905 (51)

Thus from (26) and (28) we have the scalar field as

120593 = 119888119888119871

2119890(119871119897119905)

(52)

Equations (26) and (27)rArr

119886 = 119888119898

2119890(119898119897119905)

(53)

Similarly (22) (26) and (53)rArr

119887 = 119888(3minus119898)2

2119890((3minus119898)2)119897119905

119898 = 3 (54)

From (22) and (26) the spatial volume of this model is

119881 = 1198883

2119890(3119897119905)

(55)

The directional Hubble parameters1198671 1198672= 1198673are given by

1198671= 119898119897 (56)

1198672= 1198673=

(3 minus 119898) 119897

2

(57)

Thus the mean generalized parameters defined in (23) takethe form

119867 = 119897 = constant (58)

In this case expansion scalar 120579 mean anisotropy parameter119860119898 and shear scalar are respectively given by

120579 = 3119897

119860119898=

1

2

(1198982minus 2119898 + 1)

1205902=

91198972

2

(59)

6 Advances in High Energy Physics

Using (53) and (54) Bianchi type IX cosmological model in(2) in Barberrsquos second self-creation theory takes the form

1198891199042= minus119889119905

2+ 1198882119898

2119890(2119898119897119905)

1198891199092+ 119888(3minus119898)

2119890(3minus119898)119897119905

1198891199102

+ [119888(3minus119898)

2119890(3minus119898)119897119905sin2119910 + 1198882119898

2119890(2119898119897119905)cos2119910] 1198891199112

minus 21198882119898

2119890(2119898119897119905) cos119910119889119909119889119911

(60)

In this case (15) and (54) give the energy density of themagnetic field

120588119861=

1198961

1198882(3minus119898)

21198902(3minus119898)119897119905

(61)

Using (9) with (52) (53) (54) and (61) gives the energydensity of the DE

120588 = minus

1198961

1198882(3minus119898)

2

119890minus2(3minus119898)119897119905

minus

119888119888119871

2

8120587

(9 + 6119898 minus 3119898)21198972119890(119871119897119905)

4

minus

119888(4119898minus6)

2

4

119890(4119898+119871minus6)119897119905

+ 119888(119898minus3)

2119890(119871+119898minus3)119897119905

(62)

Equation (19) with (53) (54) and (62) gives the skewnessparameter 120575(119905) as

120575 (119905) = (32120587119873 (3 minus 119898) 1198972)

times (minus321205871198961[1198882119890minus119897119905]

2(3minus119898)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+ 119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119862[1198882119890119897119905]

(119871+119898minus3)

)

minus1

(63)

and similarly (20) with (53) (54) and (62) gives the skewnessparameter 120574(119905)

120574 (119905) = (minus321205871198731198981198972)

times minus321205871198961[1198882119890119897119905]

2(119898minus3)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119888[1198882119890119897119905]

(119898+119871minus3)

minus1

(64)

Equation (17) with (53) (54) and (62) gives the EoS parame-ter 120596(119905) as

120596 (119905) = (2119898 minus 3) 1198961119897[1198882119890119897119905]

2(119898minus3)

+

119888119888119871

2

8120587

[

(3 + 119871) 1198973(9 + 6119898 minus 3119898

2) 119890(119871119897119905)

4

minus

(4119898 + 119871 minus 3) 1198971198882(2119898minus3)

2119890(4119898+119871minus6)119897119905

4

+ (119871 + 119898) 119897119888(119898minus3)

2119890(119871+119898minus3)119897119905

]

(65)

321 The Physical Behavior of the Model When 119899=0 For thismodel average scale factor 119877 = 119888

2119890119897119905 and the scalar field

120593 = 119888119888119871

2119890119871119897119905 This model is nonsingular since the exponential

function never vanishes Thus this model does not have anyphysical singularity For this model the directional Hubbleparameters as well as mean generalized Hubble parameter119867are constant throughout the evolution of the universe Hence119889119867119889119905 = 0 This implies that the greater the value of Hubbleparameter the faster the rate of expansion of the universeHence this model may represent inflationary era in the earlystages of the universe and the very late time of the universeThe spatial volume of the universe is finite when cosmic timeis zero and expands exponentially as 119905 increases and becomesinfinite when 119905 = infin which indicates that universe startsits expansion with zero volume from finite past In this casethe expansion scalar 120579 and the mean anisotropy parameter119860119898are constants throughout the evolution of the universe

but mean anisotropy parameter is exactly the same as thepreviousmodelThe energy density of themagnetic field is 120588

119861

= 11989611198882(3minus119898)

2= constant when time 119905 = 0 and119898 = 3 but when

119898 = 3 it is equal to constant 1198961 The density of the magnetic

field vanisheswhen the cosmic time is infinite Energy densityof theDE is some finite number when cosmic time is zero andit increases with increase in time and it becomes infinite whentime is infinite The skewness parameters 120575(119905) 120574(119905) as well asEoS parameters 120596(119905) are the functions of cosmic time 119905 Inthis model also lim

119905rarrinfin(120590120579)2

= 0 Hence this model doesnot approach the isotropy

In this case also we extend our work to investigate theconsistency of model (57) with the observational parametersfrom the point of astrophysical phenomena

(1) Look-Back Time Redshift From (26) and (53) we have

119867(1199050minus 119905) = log (1 + 119911) (66)

Thus for small 119911 we have

1198670(1199050minus 119905) = log (1 + 119911) = [119911 minus 119911

2

2

+ sdot sdot sdot ]

where 119905 = 1199050minus

log (1 + 119911)119867

(67)

Advances in High Energy Physics 7

(2) Luminosity Distance Redshift The luminosity distance oflight source is given by

1198670119889119871= 119911 (1 + 119911) 997904rArr 119889

119871=

119911 (1 + 119911)

119867

(68)

The above equation shows that the luminosity distanceincreases faster with the redshift when 119899 = 0

4 Conclusion

In the present paper we have discussed magnetized Bianchitype IX cosmological model in Barberrsquos second self-creationtheory We have studied the minimal interaction betweenmagnetic field and DE which will help us in detecting DEWe have obtained the exact solution of the Bianchi type IXcosmological model It is observed that in both models EoSparameter is a function of cosmic time which supportedthe recent observations The interesting and remarkableobservation of the present paper is that the mean anisotropyparameter 119860

119898for both models is the same and is constant

Also lim119905rarrinfin

(120590120579)2= 0 for bothmodels Hence bothmodels

do not approach the isotropyWe have also studied the two astrophysical phenomena

such as look-back time redshift and luminosity distanceredshift for both models and observed that such models arecompatible with recent observations because from the pointof recent astronomical measurements obtained by Pawaret al [15 16] Riess et al [17 18] and Permutter et al[19] the SN (supernovae) Hubble diagram derived from theobservations of hundreds of SNe detected over the borderrange of redshifts has amply demonstrated that the universeis expanding with acceleration Further confirmation for theaccelerating universe came from the recent observations of Iatype of SNe studied by Pawar et al [16] Tonry et al [50] andClocchiatti et al [51] Within the general relativity in orderto explain the accelerated expansion of the universe a nearlysmooth formof energy of large negative pressure is inevitableConfirmation by Bennett et al [52] regarding the filling-in ofthe universe by a dominated component of energy with largenegative pressure dubbed as dark energy was provided bythe measurements of cosmic microwave background (CMB)and large scale structure (LSS) studied by Tegmark et al [53]This formof energy is believed to account for about 75of theuniverseThe current observational data obtained by Friemanet al [54] provide strong evidence regarding the existence ofdark energy and further demonstrate that the fractional ofcritical that is being contributed by the dark energy may goas high as 076pm002

Our present model is noninteracting Bianchi type IXcosmological model which cannot resolve the coincidenceproblem since it predicts inclusive system in which magneticenergy density decreases faster (which is inversely propor-tional to scale factor) while density of the dark energy eitherremains constant or increasesThe interactingmodels play animportant role in the study of coincidence problem [55 56]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like thank the referee for invaluablesuggestions

References

[1] G A Barber ldquoOn two ldquoself-creationrdquo cosmologiesrdquo GeneralRelativity and Gravitation vol 14 no 2 pp 117ndash136 1982

[2] C Brans and R H Dicke ldquoMachrsquos principle and a relativistictheory of gravitationrdquo Physical Review vol 124 no 3 pp 925ndash935 1961

[3] C H Brans ldquoConsistency of field equations in ldquoself-creationrdquocosmologiesrdquo General Relativity and Gravitation vol 19 no 9pp 949ndash952 1987

[4] L O Pinental ldquoExact self-creation cosmological solutionsrdquoAstrophysics and Space Science vol 116 pp 395ndash399 1985

[5] R T Sing and S Deo ldquoZero-mass scalar interactions in theRobertson-Walker Universerdquo Acta Physica Hungarica vol 59no 3-4 pp 321ndash325 1986

[6] H H Soleng ldquoCosmic shear in inflationary models of Bianchitypes VIII and IXrdquo Astrophysics and Space Science vol 137 pp373ndash384 1987

[7] H H Soleng ldquoSelf-creation cosmological solutionsrdquo Astro-physics and Space Science vol 139 no 1 pp 13ndash19 1987

[8] D R K Reddy ldquoBianchi type-I vacuum model in self-creationcosmologyrdquo Astrophysics and Space Science vol 132 no 2 pp401ndash403 1987

[9] D R K Reddy ldquoVacuum friedmann model in self-creationcosmologyrdquo Astrophysics and Space Science vol 133 no 1 pp189ndash191 1987

[10] S D Maharaj and A Beesham ldquoOpen and closed Robertson-Walker-type Lyttleton-Bondi universesrdquo Astrophysics and SpaceScience vol 140 no 1 pp 33ndash37 1988

[11] R Venkateswaru and D R K Reddy ldquoBianchi type-V radiatingmodel in self creation cosmologyrdquo Astrophysics and SpaceScience vol 151 p 353 1989

[12] R Venkateswaru and D R K Reddy Astrophysics and SpaceScience 152337 1989

[13] K Shanti and V U M Rao ldquoBianchi type-II and III modelsin self-creation cosmologyrdquo Astrophysics and Space Science vol179 no 1 pp 147ndash153 1991

[14] G Mohanti and B D Pradhan ldquoCosmological mesonic viscousfluid modelrdquo International Journal of Theoretical Physics vol 1article 31 1992

[15] D D Pawar S N Bayaskar and V R Patil ldquoPlane symmetriccosmological model with thick domain walls in Brans-Dicketheory of gravitationrdquo Bulgarian Journal of Physics vol 36 pp68ndash75 2009

[16] D D Pawar S N Bayaskar and A G Deshmukh ldquoStringcosmological model in presence of massless scalar field inmodified theory of general relativityrdquo Romanian Reports ofPhysics vol 56 no 5-6 pp 842ndash848 2011

[17] A G Riess A V Filippenko P Challis et al ldquoObservationalevidence from supernovae for an accelerating universe and

8 Advances in High Energy Physics

a cosmological constantrdquo The Astronomical Journal vol 116article 1009 1998

[18] A G Riess L-G Strolger J Tonry et al ldquoType Ia supernovadiscoveries at 119911 gt 1 from the Hubble Space Telescope evidencefor past deceleration and constraints on dark energy evolutionrdquoThe Astrophysical Journal vol 607 pp 665ndash687 2004

[19] S Permutter S Gabi G Goldhaber et al ldquoMeasurements ofthe cosmological parameters omega and lambda from the first7 supernovae at 119911 ge 035rdquoThe Astrophysical Journal vol 483 p565 1997

[20] S J Permutter G Aldering M Della Valle et al ldquoDiscovery ofa supernova explosion at half the age of the Universerdquo Naturevol 391 pp 51ndash54 1998

[21] S J Permutter G Aldering G Goldhaber et al ldquoMeasurementsofΩ and Λ from 42 High-Redshift SupernovaerdquoThe Astrophys-ical Journal vol 517 no 2 p 565 1999

[22] D N Spergel L Verde H V Peiris et al ldquoFirst-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations determi-nation of cosmological parametersrdquo The Astrophysical JournalSupplement Series vol 148 no 1 p 175 2003

[23] D N Spergel R Bean O Dore et al ldquoThree-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations implica-tions for cosmologyrdquo The Astrophysical Journal SupplementSeries vol 170 no 2 article 377 2007

[24] R RCaldwell ldquoCosmicMicrowaveBackground and Supernovaconstraints on quintessence concordance regions and targetmodelsrdquo Physical Review D vol 69 2004

[25] R R Caldwell ldquoSudden gravitational transitionrdquo PhysicalReview D vol 73 2006

[26] A G Cohen D B Kaplan and A E Nelson ldquoEffective fieldtheory black holes and the cosmological constantrdquo PhysicalReview Letters vol 82 no 25 pp 4971ndash4974 1999

[27] E J Copeland M Sami and S Tsujikawa ldquoDynamics of darkenergyrdquo International Journal of Modern Physics vol 15 no 11pp 1753ndash1935 2006

[28] A Deo J S Alcaniz and D Jain ldquoCosmological consequencesof a chaplygin gas dark energyrdquo Physical Review D vol 67Article ID 023515 2004

[29] B Ratra and J Peebles ldquoFractal model for disordered magnetsrdquoPhysical Review D vol 37 p 321 1988

[30] R R Caldwell ldquoA phantom menace Cosmological conse-quences of a dark energy component with super-negativeequation of staterdquo Physics Letters B vol 545 no 1-2 pp 23ndash292002

[31] E Elizalde S Nojiri and S D Odinstov ldquoLate-time cosmologyin a (phantom) scalar-tensor theory dark energy and thecosmic speed-uprdquo Physical Review D vol 70 no 4 Article ID043539 2004

[32] A Kamenshchik U Moschella and V Pasquier ldquoAn alternativeto quintessencerdquo Physics Letters B vol 511 no 2-4 pp 265ndash2682001

[33] T Padmanabhan ldquoAccelerated expansion of the universe drivenby tachyonic matterrdquo Physical Review D vol 66 Article ID021301 2002

[34] D D Pawar Y S Solanke and S N Bayaskar ldquoKantowski-sachscosmological models with constat EoS parameter in BarberrsquosSecond Self Creation Theoryrdquo Prespacetime Journal vol 5 no2 pp 60ndash68 2014

[35] D D Pawar and Y S Solanke ldquoExact kantowski-sachsanisotropic dark energy cosmological models in brans dicke

theory of gravitationrdquo International Journal of TheoreticalPhysics vol 53 no 9 pp 3052ndash3065 2014

[36] L P Chimento ldquoExtended tachyon field Chaplygin gas andsolvable 119896-essence cosmologiesrdquo Physical Review D vol 69 no12 Article ID 123517 10 pages 2004

[37] C W Misner ldquoThe isotropy of the universerdquo The AstrophysicalJournal vol 151 p 431 1968

[38] K Land and J Maqueijo ldquoExamination of evidence for apreferred axis in the cosmic radiation anisotropyrdquo PhysicalReview Letters vol 95 Article ID 071301 2005

[39] M Demianski ldquoTilted plane symmetric magnetized cosmolog-ical modelsrdquo Physical Review D vol 46 no 4 pp 1391ndash13981992

[40] D D Pawar V D Dagwal and Y S Solanke ldquoTilted plane sym-metricmagnetized cosmological modelsrdquo Prespacetime Journalvol 5 no 2 pp 368ndash377 2014

[41] D D Pawar and V J Dagwal ldquoBianchi type IX string cos-mological model in general relativityrdquo International Journal ofTheoretical Physics vol 53 no 7 pp 2441ndash2450 2014

[42] R Bali and S Dave ldquoBianchi type IX string cosmological modelfor perfect fluid distribution in general relativityrdquo PramanaJournal of Physics vol 56 p 4 2001

[43] A Tyagi and K Sharma ldquoBianchi type IX string cosmologicalmodel for perfect fluid distribution in general relativityrdquoChinesePhysics Letters vol 27 no 7 Article ID 079801 2010

[44] V U M Rao and Y V S S Sanyasiraju ldquoExact Bianchi-typeVIII and IX models in the presence of zero-mass scalar fieldsrdquoAstrophysics and Space Science vol 187 no 1 pp 113ndash117 1992

[45] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 no 4 pp 689ndash6932013

[46] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 pp 689ndash693 2013

[47] O Akarsu and C B Kilinc ldquoLRS Bianchi type I models withanisotropic dark energy and constant deceleration parameterrdquoGeneral Relativity and Gravitation vol 42 pp 119ndash140 2010

[48] M S Berman ldquoA special law of variation for Hubblersquos parame-terrdquo Il Nuovo Cimento B vol 74 pp 182ndash186 1983

[49] V B Johri andK Desikan ldquoCosmological models with constantdeceleration parameter in Brans-Dicke theoryrdquoGeneral Relativ-ity and Gravitation vol 26 no 12 pp 1217ndash1232 1994

[50] J L Tonry B P Schmidt B Barris et al ldquoCosmological resultsfrom high-z supernovaerdquoThe Astrophysical Journal vol 594 p1 2003

[51] A Clocchiatti B P Schmidt and A V Filippenko ldquoHubbleSpace Telescope and Ground-based Observations of Type IaSupernovae at Redshift 05 Cosmological Implicationsrdquo TheAstrophysical Journal vol 642 no 1 2006

[52] C L Bennett R S Hill G Hinshaw et al ldquoFirst-yearWilkinson Microwave Anisotropy Probe (WMAP) observationsforeground emissionrdquo The Astrophysical Journal SupplementSeries vol 148 no 1 pp 97ndash117 2003

[53] M Tegmark M R Blanton M A Strauss et al ldquoThe three-dimensional power spectrum of galaxies from the sloan digitalsky surveyrdquoTheAstrophysical Journal vol 606 no 2 article 7022004

[54] J Frieman M Turner and D Huterer ldquoDark energy andthe accelerating universerdquo Annual Review of Astronomy andAstrophysics vol 46 pp 385ndash432 2008

Advances in High Energy Physics 9

[55] S del Campo C Fabris R Herrera and W Zimdahl ldquoHolo-graphic dark-energymodelsrdquo Physical Review D vol 83 ArticleID 123006 2011

[56] S del Campo R Herrera and D Pavon ldquoInteracting modelsmay be key to solve the cosmic coincidence problemrdquo Journalof Cosmology and Astroparticle Physics vol 2009 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

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Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

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GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

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Soft MatterJournal of

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AerodynamicsJournal of

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PhotonicsJournal of

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Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

4 Advances in High Energy Physics

getting exponential expansion model Further in view of theanisotropy of the space time in order to obtain determinatesolution we have to assume two more constraints as

119886 = 119877119898 (27)

where 119898 is constant and the power law relation betweenaverage scale factor119877 and the scalar field120593 (Johri andDesikan[49]) yields

120593 prop 119877119871997904rArr 120593 = 119888119877

119871 (28)

where 119871 is any integer and 119888 is the constant of proportionality

31 Power ExpansionModelWhen 119899 = 0 Average scale factorfor this model by (25) is

119877 = (119899119897119905 + 1198881)1119899 (29)

Hence the scalar field 120593 from (25) and (28) is

120593 = 119888(119899119897119905 + 1198881)119871119899 (30)

Equations (25) and (27) give

119886 = (119899119897119905 + 1198881)119898119899 (31)

From (22) (25) and (31) we have

119887 = (119899119897119905 + 1198881)(3minus119898)2119899

(32)

Equations (22) and (25) give the spatial volume as

119881 = (119899119897119905 + 1198881)3119899 (33)

The directional Hubble parameters defined by (24) take theform

1198671=

119897

(119899119897119905 + 1198881)

1198672= 1198673=

(3 minus 119898) 119897

2 (119899119897119905 + 1198881)

(34)

Hence the mean generalized Hubble parameter defined in(23) takes the form

119867 =

119897

(119899119897119905 + 1198881)

(35)

The expansion scalar 120579 mean anisotropy parameter 119860119898 and

shear scalar 120590 are respectively given by

120579 =

3119897

(119899119897119905 + 1198881)

(36)

119860119898=

(1198982minus 2119898 + 1)

2

(37)

1205902=

91198972

2(119899119897119905 + 1198881)2 (38)

Using (31) and (32) Bianchi type IX cosmologicalmodel in (2)in Barberrsquos second self-creation theory takes the form

1198891199042= minus119889119905

2+ (119899119897119905 + 119888

1)2119898119899

1198891199092+ (119899119897119905 + 119888

1)(3minus119898)119899

1198891199102

+ [(119899119897119905 + 1198881)(3minus119898)119899sin2119910 + (119899119897119905 + 119888

1)2119898119899cos2119910] 1198891199112

minus 2(119899119897119905 + 1198881)2119898119899 cos119910119889119909119889119911

(39)

Equations (15) and (31) give the energy density of magneticfield as

120588119861=

1198961

(119899119897119905 + 1198881)2(3minus119898)119899

(40)

Using (9) with (30) (31) (32) and (40) energy density of theDE is

120588 =

minus1198961

(119899119897119905 + 1198881)2(3minus119898)119899

minus

119888

8120587

3 (119898 + 1) (3 minus 119898) 1198972

4(119899119897119905 + 1198881)(2119899minus119871)119899

minus

1

4(119899119897119905 + 1198881)(2(3minus119898)minus119871)119899

+

1

(119899119897119905 + 1198881)(3minus119898minus119871)119899

(41)

Using (19) with (31) (32) and (41) skewness parameter 120575(119905)takes the form

120575 (119905) = (

32120587119873 (3 minus 119898) 1198972

(119899119897119905 + 1198881)119871119899

)

times [minus321205871198961(119899119897119905 + 119888

1)(2(119898+119899minus3)minus119871)119899

minus (9 + 6119898 minus 31198982) 1198881198972+ 119888(119899119897119905 + 119888

1)2(2119898+119899minus3)119899

minus 4119888(119899119897119905 + 1198881)[2119899minus(3minus119898minus2119871)]119899

]

minus1

(42)

Using (20) with (31) (32) and (41) the skewness parameter120574(119905) takes the form

120574 (119905) = (

minus321205871198731198981198972

(119899119897119905 + 1198881)119871119899)

times [minus321205871198961(119899119897119905 + 119888

1)(2(119898+119899minus3)minus119871)119899

minus (9 + 6119898 minus 31198982) 1198881198972+ 119888(119899119897119905 + 119888

1)2(2119898+119899minus3)119899

minus 4119888(119899119897119905 + 1198881)[2119899minus(3minus119898minus2119871)]119899

]

minus1

(43)

Advances in High Energy Physics 5

Using (17) with (31) (32) and (41) the EoS parameter of themodel is

120596 (119905) = (2119898 minus 3) 1198961119897(119899119897119905 + 119888

1)(2119898minus119899minus6)119899

+

119888

8120587

[

1198973(119898 + 1) (3 minus 119898) (9 + 3119871 minus 6119899)

4

times (119899119897119905 + 1198881)(119871minus3119899)119899

]

+

119888

8120587

[minus

(119871 + 2119898 minus 3) 119897

4

(119899119897119905 + 1198881)(2119898+119871minus119899minus6)119899

+ (119871 + 119898) 119897(119899119897119905 + 1198881)(119871+119898minus3minus119899)

]

(44)

311 Physical Behavior of the Model When 119899 = 0 In thismodel the direction the directional Hubble parameter meangeneralized Hubble parameters expansion scalar Barberrsquosscalar field and shear scalar all are the functions of the cosmictime except themean anisotropy parameter119860

119898 It is constant

throughout the universe All the above parameters vanishwhen cosmic time is infinite whereas these parametersare finite when time is zero except the directional Hubbleparameter119867

2 It follows the above property provided119898 = 3

The spatial volume of this model is also a function of cosmictime and it increases with increase in timeThat is the modelis expanding with time The energy density of the model isconstant when cosmic time zero 119898 = 3 but when 119898 = 3

the energy density of the magnetic field is 1198961and it vanishes

when 119905 is infinite The energy density of the DE is constantwhen cosmic time is zero and it tends to zero when cosmictime tends to infinite when119898 = 3 but when119898 = 3 (119871 119899 gt 0)the energy density of the DE is minus119896

1+ (311988832120587)(119899119897119905 + 119888

1)119871119899

Thus in this case the energy density of DE increases withincrease in cosmic time and when 119905 = 0 energy density ofDE is minus119896

1+ (311988832120587)119888

119871119899

1= constant Similarly the skewness

parameters 120575(119905) 120574(119905) as well as EoS parameter 120596(119905) are thefunctions of cosmic time 119905 Also lim

119905rarrinfin(120590120579)2

= 0 Hencethis model does not approach the isotropy

We now extend our work to investigate the consistency ofmodel (39) with the observational parameters from the pointof astrophysical phenomena

(1) Look-Back Time RedshiftThe look-back time 119905119871is defined

as the difference between the present age of the universe 1199050

and the age of the universe 119905 when a particular light ray atredshift 119911 was emitted

The average scale factor of the universe 119877 for a givenredshift 119911 is related to the present scale factor 119877

0by the

relation 1 + 119911 = 1198770119877

Equations (25) and (35) give

1198670(1199050minus 119905) =

1

119899

[1 minus (1 + 119911)minus119899] (45)

After little manipulation we get

1198670(1199050minus 119905) = 119911 minus

(119899 minus 1)

2

1199112+ sdot sdot sdot (46)

Taking limit 119911 rarr infin in (45) the present age of the universeis

1198670(1199050minus 119905) =

1

119899

[1 minus 0] 997904rArr 1199050=

1

1198991198670

=

119867minus1

0

119899

119899 = 0

(47)

where1198670is the present value of the Hubble parameter

(2) Luminosity Distance RedshiftThe luminosity distance 119889119871

of a light source is defined as

119889119871= 11987701199031 (119911) (1 + 119911) (48)

where the radial coordinate distance 1199031(119911) of the object at light

emission is

1199031 (119911) = int

1199050

1199051

119889119905

119877

=

119867minus1

0119877minus1

0

(119899 minus 1)

[1 minus (1 + 119911)1minus119899] (49)

Solving (48) and (49) we get

1198670119889119871=

(1 + 119911)

(119899 minus 1)

[1 minus (1 + 119911)(1minus119899)

] (50)

32 Exponential ExpansionModelWhen 119899 = 0 Average scalefactor for this model by (26) is

119877 = 1198882119890119897119905 (51)

Thus from (26) and (28) we have the scalar field as

120593 = 119888119888119871

2119890(119871119897119905)

(52)

Equations (26) and (27)rArr

119886 = 119888119898

2119890(119898119897119905)

(53)

Similarly (22) (26) and (53)rArr

119887 = 119888(3minus119898)2

2119890((3minus119898)2)119897119905

119898 = 3 (54)

From (22) and (26) the spatial volume of this model is

119881 = 1198883

2119890(3119897119905)

(55)

The directional Hubble parameters1198671 1198672= 1198673are given by

1198671= 119898119897 (56)

1198672= 1198673=

(3 minus 119898) 119897

2

(57)

Thus the mean generalized parameters defined in (23) takethe form

119867 = 119897 = constant (58)

In this case expansion scalar 120579 mean anisotropy parameter119860119898 and shear scalar are respectively given by

120579 = 3119897

119860119898=

1

2

(1198982minus 2119898 + 1)

1205902=

91198972

2

(59)

6 Advances in High Energy Physics

Using (53) and (54) Bianchi type IX cosmological model in(2) in Barberrsquos second self-creation theory takes the form

1198891199042= minus119889119905

2+ 1198882119898

2119890(2119898119897119905)

1198891199092+ 119888(3minus119898)

2119890(3minus119898)119897119905

1198891199102

+ [119888(3minus119898)

2119890(3minus119898)119897119905sin2119910 + 1198882119898

2119890(2119898119897119905)cos2119910] 1198891199112

minus 21198882119898

2119890(2119898119897119905) cos119910119889119909119889119911

(60)

In this case (15) and (54) give the energy density of themagnetic field

120588119861=

1198961

1198882(3minus119898)

21198902(3minus119898)119897119905

(61)

Using (9) with (52) (53) (54) and (61) gives the energydensity of the DE

120588 = minus

1198961

1198882(3minus119898)

2

119890minus2(3minus119898)119897119905

minus

119888119888119871

2

8120587

(9 + 6119898 minus 3119898)21198972119890(119871119897119905)

4

minus

119888(4119898minus6)

2

4

119890(4119898+119871minus6)119897119905

+ 119888(119898minus3)

2119890(119871+119898minus3)119897119905

(62)

Equation (19) with (53) (54) and (62) gives the skewnessparameter 120575(119905) as

120575 (119905) = (32120587119873 (3 minus 119898) 1198972)

times (minus321205871198961[1198882119890minus119897119905]

2(3minus119898)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+ 119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119862[1198882119890119897119905]

(119871+119898minus3)

)

minus1

(63)

and similarly (20) with (53) (54) and (62) gives the skewnessparameter 120574(119905)

120574 (119905) = (minus321205871198731198981198972)

times minus321205871198961[1198882119890119897119905]

2(119898minus3)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119888[1198882119890119897119905]

(119898+119871minus3)

minus1

(64)

Equation (17) with (53) (54) and (62) gives the EoS parame-ter 120596(119905) as

120596 (119905) = (2119898 minus 3) 1198961119897[1198882119890119897119905]

2(119898minus3)

+

119888119888119871

2

8120587

[

(3 + 119871) 1198973(9 + 6119898 minus 3119898

2) 119890(119871119897119905)

4

minus

(4119898 + 119871 minus 3) 1198971198882(2119898minus3)

2119890(4119898+119871minus6)119897119905

4

+ (119871 + 119898) 119897119888(119898minus3)

2119890(119871+119898minus3)119897119905

]

(65)

321 The Physical Behavior of the Model When 119899=0 For thismodel average scale factor 119877 = 119888

2119890119897119905 and the scalar field

120593 = 119888119888119871

2119890119871119897119905 This model is nonsingular since the exponential

function never vanishes Thus this model does not have anyphysical singularity For this model the directional Hubbleparameters as well as mean generalized Hubble parameter119867are constant throughout the evolution of the universe Hence119889119867119889119905 = 0 This implies that the greater the value of Hubbleparameter the faster the rate of expansion of the universeHence this model may represent inflationary era in the earlystages of the universe and the very late time of the universeThe spatial volume of the universe is finite when cosmic timeis zero and expands exponentially as 119905 increases and becomesinfinite when 119905 = infin which indicates that universe startsits expansion with zero volume from finite past In this casethe expansion scalar 120579 and the mean anisotropy parameter119860119898are constants throughout the evolution of the universe

but mean anisotropy parameter is exactly the same as thepreviousmodelThe energy density of themagnetic field is 120588

119861

= 11989611198882(3minus119898)

2= constant when time 119905 = 0 and119898 = 3 but when

119898 = 3 it is equal to constant 1198961 The density of the magnetic

field vanisheswhen the cosmic time is infinite Energy densityof theDE is some finite number when cosmic time is zero andit increases with increase in time and it becomes infinite whentime is infinite The skewness parameters 120575(119905) 120574(119905) as well asEoS parameters 120596(119905) are the functions of cosmic time 119905 Inthis model also lim

119905rarrinfin(120590120579)2

= 0 Hence this model doesnot approach the isotropy

In this case also we extend our work to investigate theconsistency of model (57) with the observational parametersfrom the point of astrophysical phenomena

(1) Look-Back Time Redshift From (26) and (53) we have

119867(1199050minus 119905) = log (1 + 119911) (66)

Thus for small 119911 we have

1198670(1199050minus 119905) = log (1 + 119911) = [119911 minus 119911

2

2

+ sdot sdot sdot ]

where 119905 = 1199050minus

log (1 + 119911)119867

(67)

Advances in High Energy Physics 7

(2) Luminosity Distance Redshift The luminosity distance oflight source is given by

1198670119889119871= 119911 (1 + 119911) 997904rArr 119889

119871=

119911 (1 + 119911)

119867

(68)

The above equation shows that the luminosity distanceincreases faster with the redshift when 119899 = 0

4 Conclusion

In the present paper we have discussed magnetized Bianchitype IX cosmological model in Barberrsquos second self-creationtheory We have studied the minimal interaction betweenmagnetic field and DE which will help us in detecting DEWe have obtained the exact solution of the Bianchi type IXcosmological model It is observed that in both models EoSparameter is a function of cosmic time which supportedthe recent observations The interesting and remarkableobservation of the present paper is that the mean anisotropyparameter 119860

119898for both models is the same and is constant

Also lim119905rarrinfin

(120590120579)2= 0 for bothmodels Hence bothmodels

do not approach the isotropyWe have also studied the two astrophysical phenomena

such as look-back time redshift and luminosity distanceredshift for both models and observed that such models arecompatible with recent observations because from the pointof recent astronomical measurements obtained by Pawaret al [15 16] Riess et al [17 18] and Permutter et al[19] the SN (supernovae) Hubble diagram derived from theobservations of hundreds of SNe detected over the borderrange of redshifts has amply demonstrated that the universeis expanding with acceleration Further confirmation for theaccelerating universe came from the recent observations of Iatype of SNe studied by Pawar et al [16] Tonry et al [50] andClocchiatti et al [51] Within the general relativity in orderto explain the accelerated expansion of the universe a nearlysmooth formof energy of large negative pressure is inevitableConfirmation by Bennett et al [52] regarding the filling-in ofthe universe by a dominated component of energy with largenegative pressure dubbed as dark energy was provided bythe measurements of cosmic microwave background (CMB)and large scale structure (LSS) studied by Tegmark et al [53]This formof energy is believed to account for about 75of theuniverseThe current observational data obtained by Friemanet al [54] provide strong evidence regarding the existence ofdark energy and further demonstrate that the fractional ofcritical that is being contributed by the dark energy may goas high as 076pm002

Our present model is noninteracting Bianchi type IXcosmological model which cannot resolve the coincidenceproblem since it predicts inclusive system in which magneticenergy density decreases faster (which is inversely propor-tional to scale factor) while density of the dark energy eitherremains constant or increasesThe interactingmodels play animportant role in the study of coincidence problem [55 56]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like thank the referee for invaluablesuggestions

References

[1] G A Barber ldquoOn two ldquoself-creationrdquo cosmologiesrdquo GeneralRelativity and Gravitation vol 14 no 2 pp 117ndash136 1982

[2] C Brans and R H Dicke ldquoMachrsquos principle and a relativistictheory of gravitationrdquo Physical Review vol 124 no 3 pp 925ndash935 1961

[3] C H Brans ldquoConsistency of field equations in ldquoself-creationrdquocosmologiesrdquo General Relativity and Gravitation vol 19 no 9pp 949ndash952 1987

[4] L O Pinental ldquoExact self-creation cosmological solutionsrdquoAstrophysics and Space Science vol 116 pp 395ndash399 1985

[5] R T Sing and S Deo ldquoZero-mass scalar interactions in theRobertson-Walker Universerdquo Acta Physica Hungarica vol 59no 3-4 pp 321ndash325 1986

[6] H H Soleng ldquoCosmic shear in inflationary models of Bianchitypes VIII and IXrdquo Astrophysics and Space Science vol 137 pp373ndash384 1987

[7] H H Soleng ldquoSelf-creation cosmological solutionsrdquo Astro-physics and Space Science vol 139 no 1 pp 13ndash19 1987

[8] D R K Reddy ldquoBianchi type-I vacuum model in self-creationcosmologyrdquo Astrophysics and Space Science vol 132 no 2 pp401ndash403 1987

[9] D R K Reddy ldquoVacuum friedmann model in self-creationcosmologyrdquo Astrophysics and Space Science vol 133 no 1 pp189ndash191 1987

[10] S D Maharaj and A Beesham ldquoOpen and closed Robertson-Walker-type Lyttleton-Bondi universesrdquo Astrophysics and SpaceScience vol 140 no 1 pp 33ndash37 1988

[11] R Venkateswaru and D R K Reddy ldquoBianchi type-V radiatingmodel in self creation cosmologyrdquo Astrophysics and SpaceScience vol 151 p 353 1989

[12] R Venkateswaru and D R K Reddy Astrophysics and SpaceScience 152337 1989

[13] K Shanti and V U M Rao ldquoBianchi type-II and III modelsin self-creation cosmologyrdquo Astrophysics and Space Science vol179 no 1 pp 147ndash153 1991

[14] G Mohanti and B D Pradhan ldquoCosmological mesonic viscousfluid modelrdquo International Journal of Theoretical Physics vol 1article 31 1992

[15] D D Pawar S N Bayaskar and V R Patil ldquoPlane symmetriccosmological model with thick domain walls in Brans-Dicketheory of gravitationrdquo Bulgarian Journal of Physics vol 36 pp68ndash75 2009

[16] D D Pawar S N Bayaskar and A G Deshmukh ldquoStringcosmological model in presence of massless scalar field inmodified theory of general relativityrdquo Romanian Reports ofPhysics vol 56 no 5-6 pp 842ndash848 2011

[17] A G Riess A V Filippenko P Challis et al ldquoObservationalevidence from supernovae for an accelerating universe and

8 Advances in High Energy Physics

a cosmological constantrdquo The Astronomical Journal vol 116article 1009 1998

[18] A G Riess L-G Strolger J Tonry et al ldquoType Ia supernovadiscoveries at 119911 gt 1 from the Hubble Space Telescope evidencefor past deceleration and constraints on dark energy evolutionrdquoThe Astrophysical Journal vol 607 pp 665ndash687 2004

[19] S Permutter S Gabi G Goldhaber et al ldquoMeasurements ofthe cosmological parameters omega and lambda from the first7 supernovae at 119911 ge 035rdquoThe Astrophysical Journal vol 483 p565 1997

[20] S J Permutter G Aldering M Della Valle et al ldquoDiscovery ofa supernova explosion at half the age of the Universerdquo Naturevol 391 pp 51ndash54 1998

[21] S J Permutter G Aldering G Goldhaber et al ldquoMeasurementsofΩ and Λ from 42 High-Redshift SupernovaerdquoThe Astrophys-ical Journal vol 517 no 2 p 565 1999

[22] D N Spergel L Verde H V Peiris et al ldquoFirst-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations determi-nation of cosmological parametersrdquo The Astrophysical JournalSupplement Series vol 148 no 1 p 175 2003

[23] D N Spergel R Bean O Dore et al ldquoThree-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations implica-tions for cosmologyrdquo The Astrophysical Journal SupplementSeries vol 170 no 2 article 377 2007

[24] R RCaldwell ldquoCosmicMicrowaveBackground and Supernovaconstraints on quintessence concordance regions and targetmodelsrdquo Physical Review D vol 69 2004

[25] R R Caldwell ldquoSudden gravitational transitionrdquo PhysicalReview D vol 73 2006

[26] A G Cohen D B Kaplan and A E Nelson ldquoEffective fieldtheory black holes and the cosmological constantrdquo PhysicalReview Letters vol 82 no 25 pp 4971ndash4974 1999

[27] E J Copeland M Sami and S Tsujikawa ldquoDynamics of darkenergyrdquo International Journal of Modern Physics vol 15 no 11pp 1753ndash1935 2006

[28] A Deo J S Alcaniz and D Jain ldquoCosmological consequencesof a chaplygin gas dark energyrdquo Physical Review D vol 67Article ID 023515 2004

[29] B Ratra and J Peebles ldquoFractal model for disordered magnetsrdquoPhysical Review D vol 37 p 321 1988

[30] R R Caldwell ldquoA phantom menace Cosmological conse-quences of a dark energy component with super-negativeequation of staterdquo Physics Letters B vol 545 no 1-2 pp 23ndash292002

[31] E Elizalde S Nojiri and S D Odinstov ldquoLate-time cosmologyin a (phantom) scalar-tensor theory dark energy and thecosmic speed-uprdquo Physical Review D vol 70 no 4 Article ID043539 2004

[32] A Kamenshchik U Moschella and V Pasquier ldquoAn alternativeto quintessencerdquo Physics Letters B vol 511 no 2-4 pp 265ndash2682001

[33] T Padmanabhan ldquoAccelerated expansion of the universe drivenby tachyonic matterrdquo Physical Review D vol 66 Article ID021301 2002

[34] D D Pawar Y S Solanke and S N Bayaskar ldquoKantowski-sachscosmological models with constat EoS parameter in BarberrsquosSecond Self Creation Theoryrdquo Prespacetime Journal vol 5 no2 pp 60ndash68 2014

[35] D D Pawar and Y S Solanke ldquoExact kantowski-sachsanisotropic dark energy cosmological models in brans dicke

theory of gravitationrdquo International Journal of TheoreticalPhysics vol 53 no 9 pp 3052ndash3065 2014

[36] L P Chimento ldquoExtended tachyon field Chaplygin gas andsolvable 119896-essence cosmologiesrdquo Physical Review D vol 69 no12 Article ID 123517 10 pages 2004

[37] C W Misner ldquoThe isotropy of the universerdquo The AstrophysicalJournal vol 151 p 431 1968

[38] K Land and J Maqueijo ldquoExamination of evidence for apreferred axis in the cosmic radiation anisotropyrdquo PhysicalReview Letters vol 95 Article ID 071301 2005

[39] M Demianski ldquoTilted plane symmetric magnetized cosmolog-ical modelsrdquo Physical Review D vol 46 no 4 pp 1391ndash13981992

[40] D D Pawar V D Dagwal and Y S Solanke ldquoTilted plane sym-metricmagnetized cosmological modelsrdquo Prespacetime Journalvol 5 no 2 pp 368ndash377 2014

[41] D D Pawar and V J Dagwal ldquoBianchi type IX string cos-mological model in general relativityrdquo International Journal ofTheoretical Physics vol 53 no 7 pp 2441ndash2450 2014

[42] R Bali and S Dave ldquoBianchi type IX string cosmological modelfor perfect fluid distribution in general relativityrdquo PramanaJournal of Physics vol 56 p 4 2001

[43] A Tyagi and K Sharma ldquoBianchi type IX string cosmologicalmodel for perfect fluid distribution in general relativityrdquoChinesePhysics Letters vol 27 no 7 Article ID 079801 2010

[44] V U M Rao and Y V S S Sanyasiraju ldquoExact Bianchi-typeVIII and IX models in the presence of zero-mass scalar fieldsrdquoAstrophysics and Space Science vol 187 no 1 pp 113ndash117 1992

[45] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 no 4 pp 689ndash6932013

[46] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 pp 689ndash693 2013

[47] O Akarsu and C B Kilinc ldquoLRS Bianchi type I models withanisotropic dark energy and constant deceleration parameterrdquoGeneral Relativity and Gravitation vol 42 pp 119ndash140 2010

[48] M S Berman ldquoA special law of variation for Hubblersquos parame-terrdquo Il Nuovo Cimento B vol 74 pp 182ndash186 1983

[49] V B Johri andK Desikan ldquoCosmological models with constantdeceleration parameter in Brans-Dicke theoryrdquoGeneral Relativ-ity and Gravitation vol 26 no 12 pp 1217ndash1232 1994

[50] J L Tonry B P Schmidt B Barris et al ldquoCosmological resultsfrom high-z supernovaerdquoThe Astrophysical Journal vol 594 p1 2003

[51] A Clocchiatti B P Schmidt and A V Filippenko ldquoHubbleSpace Telescope and Ground-based Observations of Type IaSupernovae at Redshift 05 Cosmological Implicationsrdquo TheAstrophysical Journal vol 642 no 1 2006

[52] C L Bennett R S Hill G Hinshaw et al ldquoFirst-yearWilkinson Microwave Anisotropy Probe (WMAP) observationsforeground emissionrdquo The Astrophysical Journal SupplementSeries vol 148 no 1 pp 97ndash117 2003

[53] M Tegmark M R Blanton M A Strauss et al ldquoThe three-dimensional power spectrum of galaxies from the sloan digitalsky surveyrdquoTheAstrophysical Journal vol 606 no 2 article 7022004

[54] J Frieman M Turner and D Huterer ldquoDark energy andthe accelerating universerdquo Annual Review of Astronomy andAstrophysics vol 46 pp 385ndash432 2008

Advances in High Energy Physics 9

[55] S del Campo C Fabris R Herrera and W Zimdahl ldquoHolo-graphic dark-energymodelsrdquo Physical Review D vol 83 ArticleID 123006 2011

[56] S del Campo R Herrera and D Pavon ldquoInteracting modelsmay be key to solve the cosmic coincidence problemrdquo Journalof Cosmology and Astroparticle Physics vol 2009 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

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AstronomyAdvances in

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Superconductivity

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Statistical MechanicsInternational Journal of

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GravityJournal of

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AstrophysicsJournal of

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Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

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Soft MatterJournal of

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AerodynamicsJournal of

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PhotonicsJournal of

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Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in High Energy Physics 5

Using (17) with (31) (32) and (41) the EoS parameter of themodel is

120596 (119905) = (2119898 minus 3) 1198961119897(119899119897119905 + 119888

1)(2119898minus119899minus6)119899

+

119888

8120587

[

1198973(119898 + 1) (3 minus 119898) (9 + 3119871 minus 6119899)

4

times (119899119897119905 + 1198881)(119871minus3119899)119899

]

+

119888

8120587

[minus

(119871 + 2119898 minus 3) 119897

4

(119899119897119905 + 1198881)(2119898+119871minus119899minus6)119899

+ (119871 + 119898) 119897(119899119897119905 + 1198881)(119871+119898minus3minus119899)

]

(44)

311 Physical Behavior of the Model When 119899 = 0 In thismodel the direction the directional Hubble parameter meangeneralized Hubble parameters expansion scalar Barberrsquosscalar field and shear scalar all are the functions of the cosmictime except themean anisotropy parameter119860

119898 It is constant

throughout the universe All the above parameters vanishwhen cosmic time is infinite whereas these parametersare finite when time is zero except the directional Hubbleparameter119867

2 It follows the above property provided119898 = 3

The spatial volume of this model is also a function of cosmictime and it increases with increase in timeThat is the modelis expanding with time The energy density of the model isconstant when cosmic time zero 119898 = 3 but when 119898 = 3

the energy density of the magnetic field is 1198961and it vanishes

when 119905 is infinite The energy density of the DE is constantwhen cosmic time is zero and it tends to zero when cosmictime tends to infinite when119898 = 3 but when119898 = 3 (119871 119899 gt 0)the energy density of the DE is minus119896

1+ (311988832120587)(119899119897119905 + 119888

1)119871119899

Thus in this case the energy density of DE increases withincrease in cosmic time and when 119905 = 0 energy density ofDE is minus119896

1+ (311988832120587)119888

119871119899

1= constant Similarly the skewness

parameters 120575(119905) 120574(119905) as well as EoS parameter 120596(119905) are thefunctions of cosmic time 119905 Also lim

119905rarrinfin(120590120579)2

= 0 Hencethis model does not approach the isotropy

We now extend our work to investigate the consistency ofmodel (39) with the observational parameters from the pointof astrophysical phenomena

(1) Look-Back Time RedshiftThe look-back time 119905119871is defined

as the difference between the present age of the universe 1199050

and the age of the universe 119905 when a particular light ray atredshift 119911 was emitted

The average scale factor of the universe 119877 for a givenredshift 119911 is related to the present scale factor 119877

0by the

relation 1 + 119911 = 1198770119877

Equations (25) and (35) give

1198670(1199050minus 119905) =

1

119899

[1 minus (1 + 119911)minus119899] (45)

After little manipulation we get

1198670(1199050minus 119905) = 119911 minus

(119899 minus 1)

2

1199112+ sdot sdot sdot (46)

Taking limit 119911 rarr infin in (45) the present age of the universeis

1198670(1199050minus 119905) =

1

119899

[1 minus 0] 997904rArr 1199050=

1

1198991198670

=

119867minus1

0

119899

119899 = 0

(47)

where1198670is the present value of the Hubble parameter

(2) Luminosity Distance RedshiftThe luminosity distance 119889119871

of a light source is defined as

119889119871= 11987701199031 (119911) (1 + 119911) (48)

where the radial coordinate distance 1199031(119911) of the object at light

emission is

1199031 (119911) = int

1199050

1199051

119889119905

119877

=

119867minus1

0119877minus1

0

(119899 minus 1)

[1 minus (1 + 119911)1minus119899] (49)

Solving (48) and (49) we get

1198670119889119871=

(1 + 119911)

(119899 minus 1)

[1 minus (1 + 119911)(1minus119899)

] (50)

32 Exponential ExpansionModelWhen 119899 = 0 Average scalefactor for this model by (26) is

119877 = 1198882119890119897119905 (51)

Thus from (26) and (28) we have the scalar field as

120593 = 119888119888119871

2119890(119871119897119905)

(52)

Equations (26) and (27)rArr

119886 = 119888119898

2119890(119898119897119905)

(53)

Similarly (22) (26) and (53)rArr

119887 = 119888(3minus119898)2

2119890((3minus119898)2)119897119905

119898 = 3 (54)

From (22) and (26) the spatial volume of this model is

119881 = 1198883

2119890(3119897119905)

(55)

The directional Hubble parameters1198671 1198672= 1198673are given by

1198671= 119898119897 (56)

1198672= 1198673=

(3 minus 119898) 119897

2

(57)

Thus the mean generalized parameters defined in (23) takethe form

119867 = 119897 = constant (58)

In this case expansion scalar 120579 mean anisotropy parameter119860119898 and shear scalar are respectively given by

120579 = 3119897

119860119898=

1

2

(1198982minus 2119898 + 1)

1205902=

91198972

2

(59)

6 Advances in High Energy Physics

Using (53) and (54) Bianchi type IX cosmological model in(2) in Barberrsquos second self-creation theory takes the form

1198891199042= minus119889119905

2+ 1198882119898

2119890(2119898119897119905)

1198891199092+ 119888(3minus119898)

2119890(3minus119898)119897119905

1198891199102

+ [119888(3minus119898)

2119890(3minus119898)119897119905sin2119910 + 1198882119898

2119890(2119898119897119905)cos2119910] 1198891199112

minus 21198882119898

2119890(2119898119897119905) cos119910119889119909119889119911

(60)

In this case (15) and (54) give the energy density of themagnetic field

120588119861=

1198961

1198882(3minus119898)

21198902(3minus119898)119897119905

(61)

Using (9) with (52) (53) (54) and (61) gives the energydensity of the DE

120588 = minus

1198961

1198882(3minus119898)

2

119890minus2(3minus119898)119897119905

minus

119888119888119871

2

8120587

(9 + 6119898 minus 3119898)21198972119890(119871119897119905)

4

minus

119888(4119898minus6)

2

4

119890(4119898+119871minus6)119897119905

+ 119888(119898minus3)

2119890(119871+119898minus3)119897119905

(62)

Equation (19) with (53) (54) and (62) gives the skewnessparameter 120575(119905) as

120575 (119905) = (32120587119873 (3 minus 119898) 1198972)

times (minus321205871198961[1198882119890minus119897119905]

2(3minus119898)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+ 119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119862[1198882119890119897119905]

(119871+119898minus3)

)

minus1

(63)

and similarly (20) with (53) (54) and (62) gives the skewnessparameter 120574(119905)

120574 (119905) = (minus321205871198731198981198972)

times minus321205871198961[1198882119890119897119905]

2(119898minus3)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119888[1198882119890119897119905]

(119898+119871minus3)

minus1

(64)

Equation (17) with (53) (54) and (62) gives the EoS parame-ter 120596(119905) as

120596 (119905) = (2119898 minus 3) 1198961119897[1198882119890119897119905]

2(119898minus3)

+

119888119888119871

2

8120587

[

(3 + 119871) 1198973(9 + 6119898 minus 3119898

2) 119890(119871119897119905)

4

minus

(4119898 + 119871 minus 3) 1198971198882(2119898minus3)

2119890(4119898+119871minus6)119897119905

4

+ (119871 + 119898) 119897119888(119898minus3)

2119890(119871+119898minus3)119897119905

]

(65)

321 The Physical Behavior of the Model When 119899=0 For thismodel average scale factor 119877 = 119888

2119890119897119905 and the scalar field

120593 = 119888119888119871

2119890119871119897119905 This model is nonsingular since the exponential

function never vanishes Thus this model does not have anyphysical singularity For this model the directional Hubbleparameters as well as mean generalized Hubble parameter119867are constant throughout the evolution of the universe Hence119889119867119889119905 = 0 This implies that the greater the value of Hubbleparameter the faster the rate of expansion of the universeHence this model may represent inflationary era in the earlystages of the universe and the very late time of the universeThe spatial volume of the universe is finite when cosmic timeis zero and expands exponentially as 119905 increases and becomesinfinite when 119905 = infin which indicates that universe startsits expansion with zero volume from finite past In this casethe expansion scalar 120579 and the mean anisotropy parameter119860119898are constants throughout the evolution of the universe

but mean anisotropy parameter is exactly the same as thepreviousmodelThe energy density of themagnetic field is 120588

119861

= 11989611198882(3minus119898)

2= constant when time 119905 = 0 and119898 = 3 but when

119898 = 3 it is equal to constant 1198961 The density of the magnetic

field vanisheswhen the cosmic time is infinite Energy densityof theDE is some finite number when cosmic time is zero andit increases with increase in time and it becomes infinite whentime is infinite The skewness parameters 120575(119905) 120574(119905) as well asEoS parameters 120596(119905) are the functions of cosmic time 119905 Inthis model also lim

119905rarrinfin(120590120579)2

= 0 Hence this model doesnot approach the isotropy

In this case also we extend our work to investigate theconsistency of model (57) with the observational parametersfrom the point of astrophysical phenomena

(1) Look-Back Time Redshift From (26) and (53) we have

119867(1199050minus 119905) = log (1 + 119911) (66)

Thus for small 119911 we have

1198670(1199050minus 119905) = log (1 + 119911) = [119911 minus 119911

2

2

+ sdot sdot sdot ]

where 119905 = 1199050minus

log (1 + 119911)119867

(67)

Advances in High Energy Physics 7

(2) Luminosity Distance Redshift The luminosity distance oflight source is given by

1198670119889119871= 119911 (1 + 119911) 997904rArr 119889

119871=

119911 (1 + 119911)

119867

(68)

The above equation shows that the luminosity distanceincreases faster with the redshift when 119899 = 0

4 Conclusion

In the present paper we have discussed magnetized Bianchitype IX cosmological model in Barberrsquos second self-creationtheory We have studied the minimal interaction betweenmagnetic field and DE which will help us in detecting DEWe have obtained the exact solution of the Bianchi type IXcosmological model It is observed that in both models EoSparameter is a function of cosmic time which supportedthe recent observations The interesting and remarkableobservation of the present paper is that the mean anisotropyparameter 119860

119898for both models is the same and is constant

Also lim119905rarrinfin

(120590120579)2= 0 for bothmodels Hence bothmodels

do not approach the isotropyWe have also studied the two astrophysical phenomena

such as look-back time redshift and luminosity distanceredshift for both models and observed that such models arecompatible with recent observations because from the pointof recent astronomical measurements obtained by Pawaret al [15 16] Riess et al [17 18] and Permutter et al[19] the SN (supernovae) Hubble diagram derived from theobservations of hundreds of SNe detected over the borderrange of redshifts has amply demonstrated that the universeis expanding with acceleration Further confirmation for theaccelerating universe came from the recent observations of Iatype of SNe studied by Pawar et al [16] Tonry et al [50] andClocchiatti et al [51] Within the general relativity in orderto explain the accelerated expansion of the universe a nearlysmooth formof energy of large negative pressure is inevitableConfirmation by Bennett et al [52] regarding the filling-in ofthe universe by a dominated component of energy with largenegative pressure dubbed as dark energy was provided bythe measurements of cosmic microwave background (CMB)and large scale structure (LSS) studied by Tegmark et al [53]This formof energy is believed to account for about 75of theuniverseThe current observational data obtained by Friemanet al [54] provide strong evidence regarding the existence ofdark energy and further demonstrate that the fractional ofcritical that is being contributed by the dark energy may goas high as 076pm002

Our present model is noninteracting Bianchi type IXcosmological model which cannot resolve the coincidenceproblem since it predicts inclusive system in which magneticenergy density decreases faster (which is inversely propor-tional to scale factor) while density of the dark energy eitherremains constant or increasesThe interactingmodels play animportant role in the study of coincidence problem [55 56]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like thank the referee for invaluablesuggestions

References

[1] G A Barber ldquoOn two ldquoself-creationrdquo cosmologiesrdquo GeneralRelativity and Gravitation vol 14 no 2 pp 117ndash136 1982

[2] C Brans and R H Dicke ldquoMachrsquos principle and a relativistictheory of gravitationrdquo Physical Review vol 124 no 3 pp 925ndash935 1961

[3] C H Brans ldquoConsistency of field equations in ldquoself-creationrdquocosmologiesrdquo General Relativity and Gravitation vol 19 no 9pp 949ndash952 1987

[4] L O Pinental ldquoExact self-creation cosmological solutionsrdquoAstrophysics and Space Science vol 116 pp 395ndash399 1985

[5] R T Sing and S Deo ldquoZero-mass scalar interactions in theRobertson-Walker Universerdquo Acta Physica Hungarica vol 59no 3-4 pp 321ndash325 1986

[6] H H Soleng ldquoCosmic shear in inflationary models of Bianchitypes VIII and IXrdquo Astrophysics and Space Science vol 137 pp373ndash384 1987

[7] H H Soleng ldquoSelf-creation cosmological solutionsrdquo Astro-physics and Space Science vol 139 no 1 pp 13ndash19 1987

[8] D R K Reddy ldquoBianchi type-I vacuum model in self-creationcosmologyrdquo Astrophysics and Space Science vol 132 no 2 pp401ndash403 1987

[9] D R K Reddy ldquoVacuum friedmann model in self-creationcosmologyrdquo Astrophysics and Space Science vol 133 no 1 pp189ndash191 1987

[10] S D Maharaj and A Beesham ldquoOpen and closed Robertson-Walker-type Lyttleton-Bondi universesrdquo Astrophysics and SpaceScience vol 140 no 1 pp 33ndash37 1988

[11] R Venkateswaru and D R K Reddy ldquoBianchi type-V radiatingmodel in self creation cosmologyrdquo Astrophysics and SpaceScience vol 151 p 353 1989

[12] R Venkateswaru and D R K Reddy Astrophysics and SpaceScience 152337 1989

[13] K Shanti and V U M Rao ldquoBianchi type-II and III modelsin self-creation cosmologyrdquo Astrophysics and Space Science vol179 no 1 pp 147ndash153 1991

[14] G Mohanti and B D Pradhan ldquoCosmological mesonic viscousfluid modelrdquo International Journal of Theoretical Physics vol 1article 31 1992

[15] D D Pawar S N Bayaskar and V R Patil ldquoPlane symmetriccosmological model with thick domain walls in Brans-Dicketheory of gravitationrdquo Bulgarian Journal of Physics vol 36 pp68ndash75 2009

[16] D D Pawar S N Bayaskar and A G Deshmukh ldquoStringcosmological model in presence of massless scalar field inmodified theory of general relativityrdquo Romanian Reports ofPhysics vol 56 no 5-6 pp 842ndash848 2011

[17] A G Riess A V Filippenko P Challis et al ldquoObservationalevidence from supernovae for an accelerating universe and

8 Advances in High Energy Physics

a cosmological constantrdquo The Astronomical Journal vol 116article 1009 1998

[18] A G Riess L-G Strolger J Tonry et al ldquoType Ia supernovadiscoveries at 119911 gt 1 from the Hubble Space Telescope evidencefor past deceleration and constraints on dark energy evolutionrdquoThe Astrophysical Journal vol 607 pp 665ndash687 2004

[19] S Permutter S Gabi G Goldhaber et al ldquoMeasurements ofthe cosmological parameters omega and lambda from the first7 supernovae at 119911 ge 035rdquoThe Astrophysical Journal vol 483 p565 1997

[20] S J Permutter G Aldering M Della Valle et al ldquoDiscovery ofa supernova explosion at half the age of the Universerdquo Naturevol 391 pp 51ndash54 1998

[21] S J Permutter G Aldering G Goldhaber et al ldquoMeasurementsofΩ and Λ from 42 High-Redshift SupernovaerdquoThe Astrophys-ical Journal vol 517 no 2 p 565 1999

[22] D N Spergel L Verde H V Peiris et al ldquoFirst-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations determi-nation of cosmological parametersrdquo The Astrophysical JournalSupplement Series vol 148 no 1 p 175 2003

[23] D N Spergel R Bean O Dore et al ldquoThree-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations implica-tions for cosmologyrdquo The Astrophysical Journal SupplementSeries vol 170 no 2 article 377 2007

[24] R RCaldwell ldquoCosmicMicrowaveBackground and Supernovaconstraints on quintessence concordance regions and targetmodelsrdquo Physical Review D vol 69 2004

[25] R R Caldwell ldquoSudden gravitational transitionrdquo PhysicalReview D vol 73 2006

[26] A G Cohen D B Kaplan and A E Nelson ldquoEffective fieldtheory black holes and the cosmological constantrdquo PhysicalReview Letters vol 82 no 25 pp 4971ndash4974 1999

[27] E J Copeland M Sami and S Tsujikawa ldquoDynamics of darkenergyrdquo International Journal of Modern Physics vol 15 no 11pp 1753ndash1935 2006

[28] A Deo J S Alcaniz and D Jain ldquoCosmological consequencesof a chaplygin gas dark energyrdquo Physical Review D vol 67Article ID 023515 2004

[29] B Ratra and J Peebles ldquoFractal model for disordered magnetsrdquoPhysical Review D vol 37 p 321 1988

[30] R R Caldwell ldquoA phantom menace Cosmological conse-quences of a dark energy component with super-negativeequation of staterdquo Physics Letters B vol 545 no 1-2 pp 23ndash292002

[31] E Elizalde S Nojiri and S D Odinstov ldquoLate-time cosmologyin a (phantom) scalar-tensor theory dark energy and thecosmic speed-uprdquo Physical Review D vol 70 no 4 Article ID043539 2004

[32] A Kamenshchik U Moschella and V Pasquier ldquoAn alternativeto quintessencerdquo Physics Letters B vol 511 no 2-4 pp 265ndash2682001

[33] T Padmanabhan ldquoAccelerated expansion of the universe drivenby tachyonic matterrdquo Physical Review D vol 66 Article ID021301 2002

[34] D D Pawar Y S Solanke and S N Bayaskar ldquoKantowski-sachscosmological models with constat EoS parameter in BarberrsquosSecond Self Creation Theoryrdquo Prespacetime Journal vol 5 no2 pp 60ndash68 2014

[35] D D Pawar and Y S Solanke ldquoExact kantowski-sachsanisotropic dark energy cosmological models in brans dicke

theory of gravitationrdquo International Journal of TheoreticalPhysics vol 53 no 9 pp 3052ndash3065 2014

[36] L P Chimento ldquoExtended tachyon field Chaplygin gas andsolvable 119896-essence cosmologiesrdquo Physical Review D vol 69 no12 Article ID 123517 10 pages 2004

[37] C W Misner ldquoThe isotropy of the universerdquo The AstrophysicalJournal vol 151 p 431 1968

[38] K Land and J Maqueijo ldquoExamination of evidence for apreferred axis in the cosmic radiation anisotropyrdquo PhysicalReview Letters vol 95 Article ID 071301 2005

[39] M Demianski ldquoTilted plane symmetric magnetized cosmolog-ical modelsrdquo Physical Review D vol 46 no 4 pp 1391ndash13981992

[40] D D Pawar V D Dagwal and Y S Solanke ldquoTilted plane sym-metricmagnetized cosmological modelsrdquo Prespacetime Journalvol 5 no 2 pp 368ndash377 2014

[41] D D Pawar and V J Dagwal ldquoBianchi type IX string cos-mological model in general relativityrdquo International Journal ofTheoretical Physics vol 53 no 7 pp 2441ndash2450 2014

[42] R Bali and S Dave ldquoBianchi type IX string cosmological modelfor perfect fluid distribution in general relativityrdquo PramanaJournal of Physics vol 56 p 4 2001

[43] A Tyagi and K Sharma ldquoBianchi type IX string cosmologicalmodel for perfect fluid distribution in general relativityrdquoChinesePhysics Letters vol 27 no 7 Article ID 079801 2010

[44] V U M Rao and Y V S S Sanyasiraju ldquoExact Bianchi-typeVIII and IX models in the presence of zero-mass scalar fieldsrdquoAstrophysics and Space Science vol 187 no 1 pp 113ndash117 1992

[45] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 no 4 pp 689ndash6932013

[46] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 pp 689ndash693 2013

[47] O Akarsu and C B Kilinc ldquoLRS Bianchi type I models withanisotropic dark energy and constant deceleration parameterrdquoGeneral Relativity and Gravitation vol 42 pp 119ndash140 2010

[48] M S Berman ldquoA special law of variation for Hubblersquos parame-terrdquo Il Nuovo Cimento B vol 74 pp 182ndash186 1983

[49] V B Johri andK Desikan ldquoCosmological models with constantdeceleration parameter in Brans-Dicke theoryrdquoGeneral Relativ-ity and Gravitation vol 26 no 12 pp 1217ndash1232 1994

[50] J L Tonry B P Schmidt B Barris et al ldquoCosmological resultsfrom high-z supernovaerdquoThe Astrophysical Journal vol 594 p1 2003

[51] A Clocchiatti B P Schmidt and A V Filippenko ldquoHubbleSpace Telescope and Ground-based Observations of Type IaSupernovae at Redshift 05 Cosmological Implicationsrdquo TheAstrophysical Journal vol 642 no 1 2006

[52] C L Bennett R S Hill G Hinshaw et al ldquoFirst-yearWilkinson Microwave Anisotropy Probe (WMAP) observationsforeground emissionrdquo The Astrophysical Journal SupplementSeries vol 148 no 1 pp 97ndash117 2003

[53] M Tegmark M R Blanton M A Strauss et al ldquoThe three-dimensional power spectrum of galaxies from the sloan digitalsky surveyrdquoTheAstrophysical Journal vol 606 no 2 article 7022004

[54] J Frieman M Turner and D Huterer ldquoDark energy andthe accelerating universerdquo Annual Review of Astronomy andAstrophysics vol 46 pp 385ndash432 2008

Advances in High Energy Physics 9

[55] S del Campo C Fabris R Herrera and W Zimdahl ldquoHolo-graphic dark-energymodelsrdquo Physical Review D vol 83 ArticleID 123006 2011

[56] S del Campo R Herrera and D Pavon ldquoInteracting modelsmay be key to solve the cosmic coincidence problemrdquo Journalof Cosmology and Astroparticle Physics vol 2009 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

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PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

6 Advances in High Energy Physics

Using (53) and (54) Bianchi type IX cosmological model in(2) in Barberrsquos second self-creation theory takes the form

1198891199042= minus119889119905

2+ 1198882119898

2119890(2119898119897119905)

1198891199092+ 119888(3minus119898)

2119890(3minus119898)119897119905

1198891199102

+ [119888(3minus119898)

2119890(3minus119898)119897119905sin2119910 + 1198882119898

2119890(2119898119897119905)cos2119910] 1198891199112

minus 21198882119898

2119890(2119898119897119905) cos119910119889119909119889119911

(60)

In this case (15) and (54) give the energy density of themagnetic field

120588119861=

1198961

1198882(3minus119898)

21198902(3minus119898)119897119905

(61)

Using (9) with (52) (53) (54) and (61) gives the energydensity of the DE

120588 = minus

1198961

1198882(3minus119898)

2

119890minus2(3minus119898)119897119905

minus

119888119888119871

2

8120587

(9 + 6119898 minus 3119898)21198972119890(119871119897119905)

4

minus

119888(4119898minus6)

2

4

119890(4119898+119871minus6)119897119905

+ 119888(119898minus3)

2119890(119871+119898minus3)119897119905

(62)

Equation (19) with (53) (54) and (62) gives the skewnessparameter 120575(119905) as

120575 (119905) = (32120587119873 (3 minus 119898) 1198972)

times (minus321205871198961[1198882119890minus119897119905]

2(3minus119898)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+ 119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119862[1198882119890119897119905]

(119871+119898minus3)

)

minus1

(63)

and similarly (20) with (53) (54) and (62) gives the skewnessparameter 120574(119905)

120574 (119905) = (minus321205871198731198981198972)

times minus321205871198961[1198882119890119897119905]

2(119898minus3)

minus (9 + 6119898 minus 31198982) 119888119888119871

21198972119890(119871119897119905)

+119888[1198882119890119897119905]

(4119898+119871minus6)

minus 4119888[1198882119890119897119905]

(119898+119871minus3)

minus1

(64)

Equation (17) with (53) (54) and (62) gives the EoS parame-ter 120596(119905) as

120596 (119905) = (2119898 minus 3) 1198961119897[1198882119890119897119905]

2(119898minus3)

+

119888119888119871

2

8120587

[

(3 + 119871) 1198973(9 + 6119898 minus 3119898

2) 119890(119871119897119905)

4

minus

(4119898 + 119871 minus 3) 1198971198882(2119898minus3)

2119890(4119898+119871minus6)119897119905

4

+ (119871 + 119898) 119897119888(119898minus3)

2119890(119871+119898minus3)119897119905

]

(65)

321 The Physical Behavior of the Model When 119899=0 For thismodel average scale factor 119877 = 119888

2119890119897119905 and the scalar field

120593 = 119888119888119871

2119890119871119897119905 This model is nonsingular since the exponential

function never vanishes Thus this model does not have anyphysical singularity For this model the directional Hubbleparameters as well as mean generalized Hubble parameter119867are constant throughout the evolution of the universe Hence119889119867119889119905 = 0 This implies that the greater the value of Hubbleparameter the faster the rate of expansion of the universeHence this model may represent inflationary era in the earlystages of the universe and the very late time of the universeThe spatial volume of the universe is finite when cosmic timeis zero and expands exponentially as 119905 increases and becomesinfinite when 119905 = infin which indicates that universe startsits expansion with zero volume from finite past In this casethe expansion scalar 120579 and the mean anisotropy parameter119860119898are constants throughout the evolution of the universe

but mean anisotropy parameter is exactly the same as thepreviousmodelThe energy density of themagnetic field is 120588

119861

= 11989611198882(3minus119898)

2= constant when time 119905 = 0 and119898 = 3 but when

119898 = 3 it is equal to constant 1198961 The density of the magnetic

field vanisheswhen the cosmic time is infinite Energy densityof theDE is some finite number when cosmic time is zero andit increases with increase in time and it becomes infinite whentime is infinite The skewness parameters 120575(119905) 120574(119905) as well asEoS parameters 120596(119905) are the functions of cosmic time 119905 Inthis model also lim

119905rarrinfin(120590120579)2

= 0 Hence this model doesnot approach the isotropy

In this case also we extend our work to investigate theconsistency of model (57) with the observational parametersfrom the point of astrophysical phenomena

(1) Look-Back Time Redshift From (26) and (53) we have

119867(1199050minus 119905) = log (1 + 119911) (66)

Thus for small 119911 we have

1198670(1199050minus 119905) = log (1 + 119911) = [119911 minus 119911

2

2

+ sdot sdot sdot ]

where 119905 = 1199050minus

log (1 + 119911)119867

(67)

Advances in High Energy Physics 7

(2) Luminosity Distance Redshift The luminosity distance oflight source is given by

1198670119889119871= 119911 (1 + 119911) 997904rArr 119889

119871=

119911 (1 + 119911)

119867

(68)

The above equation shows that the luminosity distanceincreases faster with the redshift when 119899 = 0

4 Conclusion

In the present paper we have discussed magnetized Bianchitype IX cosmological model in Barberrsquos second self-creationtheory We have studied the minimal interaction betweenmagnetic field and DE which will help us in detecting DEWe have obtained the exact solution of the Bianchi type IXcosmological model It is observed that in both models EoSparameter is a function of cosmic time which supportedthe recent observations The interesting and remarkableobservation of the present paper is that the mean anisotropyparameter 119860

119898for both models is the same and is constant

Also lim119905rarrinfin

(120590120579)2= 0 for bothmodels Hence bothmodels

do not approach the isotropyWe have also studied the two astrophysical phenomena

such as look-back time redshift and luminosity distanceredshift for both models and observed that such models arecompatible with recent observations because from the pointof recent astronomical measurements obtained by Pawaret al [15 16] Riess et al [17 18] and Permutter et al[19] the SN (supernovae) Hubble diagram derived from theobservations of hundreds of SNe detected over the borderrange of redshifts has amply demonstrated that the universeis expanding with acceleration Further confirmation for theaccelerating universe came from the recent observations of Iatype of SNe studied by Pawar et al [16] Tonry et al [50] andClocchiatti et al [51] Within the general relativity in orderto explain the accelerated expansion of the universe a nearlysmooth formof energy of large negative pressure is inevitableConfirmation by Bennett et al [52] regarding the filling-in ofthe universe by a dominated component of energy with largenegative pressure dubbed as dark energy was provided bythe measurements of cosmic microwave background (CMB)and large scale structure (LSS) studied by Tegmark et al [53]This formof energy is believed to account for about 75of theuniverseThe current observational data obtained by Friemanet al [54] provide strong evidence regarding the existence ofdark energy and further demonstrate that the fractional ofcritical that is being contributed by the dark energy may goas high as 076pm002

Our present model is noninteracting Bianchi type IXcosmological model which cannot resolve the coincidenceproblem since it predicts inclusive system in which magneticenergy density decreases faster (which is inversely propor-tional to scale factor) while density of the dark energy eitherremains constant or increasesThe interactingmodels play animportant role in the study of coincidence problem [55 56]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like thank the referee for invaluablesuggestions

References

[1] G A Barber ldquoOn two ldquoself-creationrdquo cosmologiesrdquo GeneralRelativity and Gravitation vol 14 no 2 pp 117ndash136 1982

[2] C Brans and R H Dicke ldquoMachrsquos principle and a relativistictheory of gravitationrdquo Physical Review vol 124 no 3 pp 925ndash935 1961

[3] C H Brans ldquoConsistency of field equations in ldquoself-creationrdquocosmologiesrdquo General Relativity and Gravitation vol 19 no 9pp 949ndash952 1987

[4] L O Pinental ldquoExact self-creation cosmological solutionsrdquoAstrophysics and Space Science vol 116 pp 395ndash399 1985

[5] R T Sing and S Deo ldquoZero-mass scalar interactions in theRobertson-Walker Universerdquo Acta Physica Hungarica vol 59no 3-4 pp 321ndash325 1986

[6] H H Soleng ldquoCosmic shear in inflationary models of Bianchitypes VIII and IXrdquo Astrophysics and Space Science vol 137 pp373ndash384 1987

[7] H H Soleng ldquoSelf-creation cosmological solutionsrdquo Astro-physics and Space Science vol 139 no 1 pp 13ndash19 1987

[8] D R K Reddy ldquoBianchi type-I vacuum model in self-creationcosmologyrdquo Astrophysics and Space Science vol 132 no 2 pp401ndash403 1987

[9] D R K Reddy ldquoVacuum friedmann model in self-creationcosmologyrdquo Astrophysics and Space Science vol 133 no 1 pp189ndash191 1987

[10] S D Maharaj and A Beesham ldquoOpen and closed Robertson-Walker-type Lyttleton-Bondi universesrdquo Astrophysics and SpaceScience vol 140 no 1 pp 33ndash37 1988

[11] R Venkateswaru and D R K Reddy ldquoBianchi type-V radiatingmodel in self creation cosmologyrdquo Astrophysics and SpaceScience vol 151 p 353 1989

[12] R Venkateswaru and D R K Reddy Astrophysics and SpaceScience 152337 1989

[13] K Shanti and V U M Rao ldquoBianchi type-II and III modelsin self-creation cosmologyrdquo Astrophysics and Space Science vol179 no 1 pp 147ndash153 1991

[14] G Mohanti and B D Pradhan ldquoCosmological mesonic viscousfluid modelrdquo International Journal of Theoretical Physics vol 1article 31 1992

[15] D D Pawar S N Bayaskar and V R Patil ldquoPlane symmetriccosmological model with thick domain walls in Brans-Dicketheory of gravitationrdquo Bulgarian Journal of Physics vol 36 pp68ndash75 2009

[16] D D Pawar S N Bayaskar and A G Deshmukh ldquoStringcosmological model in presence of massless scalar field inmodified theory of general relativityrdquo Romanian Reports ofPhysics vol 56 no 5-6 pp 842ndash848 2011

[17] A G Riess A V Filippenko P Challis et al ldquoObservationalevidence from supernovae for an accelerating universe and

8 Advances in High Energy Physics

a cosmological constantrdquo The Astronomical Journal vol 116article 1009 1998

[18] A G Riess L-G Strolger J Tonry et al ldquoType Ia supernovadiscoveries at 119911 gt 1 from the Hubble Space Telescope evidencefor past deceleration and constraints on dark energy evolutionrdquoThe Astrophysical Journal vol 607 pp 665ndash687 2004

[19] S Permutter S Gabi G Goldhaber et al ldquoMeasurements ofthe cosmological parameters omega and lambda from the first7 supernovae at 119911 ge 035rdquoThe Astrophysical Journal vol 483 p565 1997

[20] S J Permutter G Aldering M Della Valle et al ldquoDiscovery ofa supernova explosion at half the age of the Universerdquo Naturevol 391 pp 51ndash54 1998

[21] S J Permutter G Aldering G Goldhaber et al ldquoMeasurementsofΩ and Λ from 42 High-Redshift SupernovaerdquoThe Astrophys-ical Journal vol 517 no 2 p 565 1999

[22] D N Spergel L Verde H V Peiris et al ldquoFirst-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations determi-nation of cosmological parametersrdquo The Astrophysical JournalSupplement Series vol 148 no 1 p 175 2003

[23] D N Spergel R Bean O Dore et al ldquoThree-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations implica-tions for cosmologyrdquo The Astrophysical Journal SupplementSeries vol 170 no 2 article 377 2007

[24] R RCaldwell ldquoCosmicMicrowaveBackground and Supernovaconstraints on quintessence concordance regions and targetmodelsrdquo Physical Review D vol 69 2004

[25] R R Caldwell ldquoSudden gravitational transitionrdquo PhysicalReview D vol 73 2006

[26] A G Cohen D B Kaplan and A E Nelson ldquoEffective fieldtheory black holes and the cosmological constantrdquo PhysicalReview Letters vol 82 no 25 pp 4971ndash4974 1999

[27] E J Copeland M Sami and S Tsujikawa ldquoDynamics of darkenergyrdquo International Journal of Modern Physics vol 15 no 11pp 1753ndash1935 2006

[28] A Deo J S Alcaniz and D Jain ldquoCosmological consequencesof a chaplygin gas dark energyrdquo Physical Review D vol 67Article ID 023515 2004

[29] B Ratra and J Peebles ldquoFractal model for disordered magnetsrdquoPhysical Review D vol 37 p 321 1988

[30] R R Caldwell ldquoA phantom menace Cosmological conse-quences of a dark energy component with super-negativeequation of staterdquo Physics Letters B vol 545 no 1-2 pp 23ndash292002

[31] E Elizalde S Nojiri and S D Odinstov ldquoLate-time cosmologyin a (phantom) scalar-tensor theory dark energy and thecosmic speed-uprdquo Physical Review D vol 70 no 4 Article ID043539 2004

[32] A Kamenshchik U Moschella and V Pasquier ldquoAn alternativeto quintessencerdquo Physics Letters B vol 511 no 2-4 pp 265ndash2682001

[33] T Padmanabhan ldquoAccelerated expansion of the universe drivenby tachyonic matterrdquo Physical Review D vol 66 Article ID021301 2002

[34] D D Pawar Y S Solanke and S N Bayaskar ldquoKantowski-sachscosmological models with constat EoS parameter in BarberrsquosSecond Self Creation Theoryrdquo Prespacetime Journal vol 5 no2 pp 60ndash68 2014

[35] D D Pawar and Y S Solanke ldquoExact kantowski-sachsanisotropic dark energy cosmological models in brans dicke

theory of gravitationrdquo International Journal of TheoreticalPhysics vol 53 no 9 pp 3052ndash3065 2014

[36] L P Chimento ldquoExtended tachyon field Chaplygin gas andsolvable 119896-essence cosmologiesrdquo Physical Review D vol 69 no12 Article ID 123517 10 pages 2004

[37] C W Misner ldquoThe isotropy of the universerdquo The AstrophysicalJournal vol 151 p 431 1968

[38] K Land and J Maqueijo ldquoExamination of evidence for apreferred axis in the cosmic radiation anisotropyrdquo PhysicalReview Letters vol 95 Article ID 071301 2005

[39] M Demianski ldquoTilted plane symmetric magnetized cosmolog-ical modelsrdquo Physical Review D vol 46 no 4 pp 1391ndash13981992

[40] D D Pawar V D Dagwal and Y S Solanke ldquoTilted plane sym-metricmagnetized cosmological modelsrdquo Prespacetime Journalvol 5 no 2 pp 368ndash377 2014

[41] D D Pawar and V J Dagwal ldquoBianchi type IX string cos-mological model in general relativityrdquo International Journal ofTheoretical Physics vol 53 no 7 pp 2441ndash2450 2014

[42] R Bali and S Dave ldquoBianchi type IX string cosmological modelfor perfect fluid distribution in general relativityrdquo PramanaJournal of Physics vol 56 p 4 2001

[43] A Tyagi and K Sharma ldquoBianchi type IX string cosmologicalmodel for perfect fluid distribution in general relativityrdquoChinesePhysics Letters vol 27 no 7 Article ID 079801 2010

[44] V U M Rao and Y V S S Sanyasiraju ldquoExact Bianchi-typeVIII and IX models in the presence of zero-mass scalar fieldsrdquoAstrophysics and Space Science vol 187 no 1 pp 113ndash117 1992

[45] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 no 4 pp 689ndash6932013

[46] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 pp 689ndash693 2013

[47] O Akarsu and C B Kilinc ldquoLRS Bianchi type I models withanisotropic dark energy and constant deceleration parameterrdquoGeneral Relativity and Gravitation vol 42 pp 119ndash140 2010

[48] M S Berman ldquoA special law of variation for Hubblersquos parame-terrdquo Il Nuovo Cimento B vol 74 pp 182ndash186 1983

[49] V B Johri andK Desikan ldquoCosmological models with constantdeceleration parameter in Brans-Dicke theoryrdquoGeneral Relativ-ity and Gravitation vol 26 no 12 pp 1217ndash1232 1994

[50] J L Tonry B P Schmidt B Barris et al ldquoCosmological resultsfrom high-z supernovaerdquoThe Astrophysical Journal vol 594 p1 2003

[51] A Clocchiatti B P Schmidt and A V Filippenko ldquoHubbleSpace Telescope and Ground-based Observations of Type IaSupernovae at Redshift 05 Cosmological Implicationsrdquo TheAstrophysical Journal vol 642 no 1 2006

[52] C L Bennett R S Hill G Hinshaw et al ldquoFirst-yearWilkinson Microwave Anisotropy Probe (WMAP) observationsforeground emissionrdquo The Astrophysical Journal SupplementSeries vol 148 no 1 pp 97ndash117 2003

[53] M Tegmark M R Blanton M A Strauss et al ldquoThe three-dimensional power spectrum of galaxies from the sloan digitalsky surveyrdquoTheAstrophysical Journal vol 606 no 2 article 7022004

[54] J Frieman M Turner and D Huterer ldquoDark energy andthe accelerating universerdquo Annual Review of Astronomy andAstrophysics vol 46 pp 385ndash432 2008

Advances in High Energy Physics 9

[55] S del Campo C Fabris R Herrera and W Zimdahl ldquoHolo-graphic dark-energymodelsrdquo Physical Review D vol 83 ArticleID 123006 2011

[56] S del Campo R Herrera and D Pavon ldquoInteracting modelsmay be key to solve the cosmic coincidence problemrdquo Journalof Cosmology and Astroparticle Physics vol 2009 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in High Energy Physics 7

(2) Luminosity Distance Redshift The luminosity distance oflight source is given by

1198670119889119871= 119911 (1 + 119911) 997904rArr 119889

119871=

119911 (1 + 119911)

119867

(68)

The above equation shows that the luminosity distanceincreases faster with the redshift when 119899 = 0

4 Conclusion

In the present paper we have discussed magnetized Bianchitype IX cosmological model in Barberrsquos second self-creationtheory We have studied the minimal interaction betweenmagnetic field and DE which will help us in detecting DEWe have obtained the exact solution of the Bianchi type IXcosmological model It is observed that in both models EoSparameter is a function of cosmic time which supportedthe recent observations The interesting and remarkableobservation of the present paper is that the mean anisotropyparameter 119860

119898for both models is the same and is constant

Also lim119905rarrinfin

(120590120579)2= 0 for bothmodels Hence bothmodels

do not approach the isotropyWe have also studied the two astrophysical phenomena

such as look-back time redshift and luminosity distanceredshift for both models and observed that such models arecompatible with recent observations because from the pointof recent astronomical measurements obtained by Pawaret al [15 16] Riess et al [17 18] and Permutter et al[19] the SN (supernovae) Hubble diagram derived from theobservations of hundreds of SNe detected over the borderrange of redshifts has amply demonstrated that the universeis expanding with acceleration Further confirmation for theaccelerating universe came from the recent observations of Iatype of SNe studied by Pawar et al [16] Tonry et al [50] andClocchiatti et al [51] Within the general relativity in orderto explain the accelerated expansion of the universe a nearlysmooth formof energy of large negative pressure is inevitableConfirmation by Bennett et al [52] regarding the filling-in ofthe universe by a dominated component of energy with largenegative pressure dubbed as dark energy was provided bythe measurements of cosmic microwave background (CMB)and large scale structure (LSS) studied by Tegmark et al [53]This formof energy is believed to account for about 75of theuniverseThe current observational data obtained by Friemanet al [54] provide strong evidence regarding the existence ofdark energy and further demonstrate that the fractional ofcritical that is being contributed by the dark energy may goas high as 076pm002

Our present model is noninteracting Bianchi type IXcosmological model which cannot resolve the coincidenceproblem since it predicts inclusive system in which magneticenergy density decreases faster (which is inversely propor-tional to scale factor) while density of the dark energy eitherremains constant or increasesThe interactingmodels play animportant role in the study of coincidence problem [55 56]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like thank the referee for invaluablesuggestions

References

[1] G A Barber ldquoOn two ldquoself-creationrdquo cosmologiesrdquo GeneralRelativity and Gravitation vol 14 no 2 pp 117ndash136 1982

[2] C Brans and R H Dicke ldquoMachrsquos principle and a relativistictheory of gravitationrdquo Physical Review vol 124 no 3 pp 925ndash935 1961

[3] C H Brans ldquoConsistency of field equations in ldquoself-creationrdquocosmologiesrdquo General Relativity and Gravitation vol 19 no 9pp 949ndash952 1987

[4] L O Pinental ldquoExact self-creation cosmological solutionsrdquoAstrophysics and Space Science vol 116 pp 395ndash399 1985

[5] R T Sing and S Deo ldquoZero-mass scalar interactions in theRobertson-Walker Universerdquo Acta Physica Hungarica vol 59no 3-4 pp 321ndash325 1986

[6] H H Soleng ldquoCosmic shear in inflationary models of Bianchitypes VIII and IXrdquo Astrophysics and Space Science vol 137 pp373ndash384 1987

[7] H H Soleng ldquoSelf-creation cosmological solutionsrdquo Astro-physics and Space Science vol 139 no 1 pp 13ndash19 1987

[8] D R K Reddy ldquoBianchi type-I vacuum model in self-creationcosmologyrdquo Astrophysics and Space Science vol 132 no 2 pp401ndash403 1987

[9] D R K Reddy ldquoVacuum friedmann model in self-creationcosmologyrdquo Astrophysics and Space Science vol 133 no 1 pp189ndash191 1987

[10] S D Maharaj and A Beesham ldquoOpen and closed Robertson-Walker-type Lyttleton-Bondi universesrdquo Astrophysics and SpaceScience vol 140 no 1 pp 33ndash37 1988

[11] R Venkateswaru and D R K Reddy ldquoBianchi type-V radiatingmodel in self creation cosmologyrdquo Astrophysics and SpaceScience vol 151 p 353 1989

[12] R Venkateswaru and D R K Reddy Astrophysics and SpaceScience 152337 1989

[13] K Shanti and V U M Rao ldquoBianchi type-II and III modelsin self-creation cosmologyrdquo Astrophysics and Space Science vol179 no 1 pp 147ndash153 1991

[14] G Mohanti and B D Pradhan ldquoCosmological mesonic viscousfluid modelrdquo International Journal of Theoretical Physics vol 1article 31 1992

[15] D D Pawar S N Bayaskar and V R Patil ldquoPlane symmetriccosmological model with thick domain walls in Brans-Dicketheory of gravitationrdquo Bulgarian Journal of Physics vol 36 pp68ndash75 2009

[16] D D Pawar S N Bayaskar and A G Deshmukh ldquoStringcosmological model in presence of massless scalar field inmodified theory of general relativityrdquo Romanian Reports ofPhysics vol 56 no 5-6 pp 842ndash848 2011

[17] A G Riess A V Filippenko P Challis et al ldquoObservationalevidence from supernovae for an accelerating universe and

8 Advances in High Energy Physics

a cosmological constantrdquo The Astronomical Journal vol 116article 1009 1998

[18] A G Riess L-G Strolger J Tonry et al ldquoType Ia supernovadiscoveries at 119911 gt 1 from the Hubble Space Telescope evidencefor past deceleration and constraints on dark energy evolutionrdquoThe Astrophysical Journal vol 607 pp 665ndash687 2004

[19] S Permutter S Gabi G Goldhaber et al ldquoMeasurements ofthe cosmological parameters omega and lambda from the first7 supernovae at 119911 ge 035rdquoThe Astrophysical Journal vol 483 p565 1997

[20] S J Permutter G Aldering M Della Valle et al ldquoDiscovery ofa supernova explosion at half the age of the Universerdquo Naturevol 391 pp 51ndash54 1998

[21] S J Permutter G Aldering G Goldhaber et al ldquoMeasurementsofΩ and Λ from 42 High-Redshift SupernovaerdquoThe Astrophys-ical Journal vol 517 no 2 p 565 1999

[22] D N Spergel L Verde H V Peiris et al ldquoFirst-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations determi-nation of cosmological parametersrdquo The Astrophysical JournalSupplement Series vol 148 no 1 p 175 2003

[23] D N Spergel R Bean O Dore et al ldquoThree-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations implica-tions for cosmologyrdquo The Astrophysical Journal SupplementSeries vol 170 no 2 article 377 2007

[24] R RCaldwell ldquoCosmicMicrowaveBackground and Supernovaconstraints on quintessence concordance regions and targetmodelsrdquo Physical Review D vol 69 2004

[25] R R Caldwell ldquoSudden gravitational transitionrdquo PhysicalReview D vol 73 2006

[26] A G Cohen D B Kaplan and A E Nelson ldquoEffective fieldtheory black holes and the cosmological constantrdquo PhysicalReview Letters vol 82 no 25 pp 4971ndash4974 1999

[27] E J Copeland M Sami and S Tsujikawa ldquoDynamics of darkenergyrdquo International Journal of Modern Physics vol 15 no 11pp 1753ndash1935 2006

[28] A Deo J S Alcaniz and D Jain ldquoCosmological consequencesof a chaplygin gas dark energyrdquo Physical Review D vol 67Article ID 023515 2004

[29] B Ratra and J Peebles ldquoFractal model for disordered magnetsrdquoPhysical Review D vol 37 p 321 1988

[30] R R Caldwell ldquoA phantom menace Cosmological conse-quences of a dark energy component with super-negativeequation of staterdquo Physics Letters B vol 545 no 1-2 pp 23ndash292002

[31] E Elizalde S Nojiri and S D Odinstov ldquoLate-time cosmologyin a (phantom) scalar-tensor theory dark energy and thecosmic speed-uprdquo Physical Review D vol 70 no 4 Article ID043539 2004

[32] A Kamenshchik U Moschella and V Pasquier ldquoAn alternativeto quintessencerdquo Physics Letters B vol 511 no 2-4 pp 265ndash2682001

[33] T Padmanabhan ldquoAccelerated expansion of the universe drivenby tachyonic matterrdquo Physical Review D vol 66 Article ID021301 2002

[34] D D Pawar Y S Solanke and S N Bayaskar ldquoKantowski-sachscosmological models with constat EoS parameter in BarberrsquosSecond Self Creation Theoryrdquo Prespacetime Journal vol 5 no2 pp 60ndash68 2014

[35] D D Pawar and Y S Solanke ldquoExact kantowski-sachsanisotropic dark energy cosmological models in brans dicke

theory of gravitationrdquo International Journal of TheoreticalPhysics vol 53 no 9 pp 3052ndash3065 2014

[36] L P Chimento ldquoExtended tachyon field Chaplygin gas andsolvable 119896-essence cosmologiesrdquo Physical Review D vol 69 no12 Article ID 123517 10 pages 2004

[37] C W Misner ldquoThe isotropy of the universerdquo The AstrophysicalJournal vol 151 p 431 1968

[38] K Land and J Maqueijo ldquoExamination of evidence for apreferred axis in the cosmic radiation anisotropyrdquo PhysicalReview Letters vol 95 Article ID 071301 2005

[39] M Demianski ldquoTilted plane symmetric magnetized cosmolog-ical modelsrdquo Physical Review D vol 46 no 4 pp 1391ndash13981992

[40] D D Pawar V D Dagwal and Y S Solanke ldquoTilted plane sym-metricmagnetized cosmological modelsrdquo Prespacetime Journalvol 5 no 2 pp 368ndash377 2014

[41] D D Pawar and V J Dagwal ldquoBianchi type IX string cos-mological model in general relativityrdquo International Journal ofTheoretical Physics vol 53 no 7 pp 2441ndash2450 2014

[42] R Bali and S Dave ldquoBianchi type IX string cosmological modelfor perfect fluid distribution in general relativityrdquo PramanaJournal of Physics vol 56 p 4 2001

[43] A Tyagi and K Sharma ldquoBianchi type IX string cosmologicalmodel for perfect fluid distribution in general relativityrdquoChinesePhysics Letters vol 27 no 7 Article ID 079801 2010

[44] V U M Rao and Y V S S Sanyasiraju ldquoExact Bianchi-typeVIII and IX models in the presence of zero-mass scalar fieldsrdquoAstrophysics and Space Science vol 187 no 1 pp 113ndash117 1992

[45] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 no 4 pp 689ndash6932013

[46] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 pp 689ndash693 2013

[47] O Akarsu and C B Kilinc ldquoLRS Bianchi type I models withanisotropic dark energy and constant deceleration parameterrdquoGeneral Relativity and Gravitation vol 42 pp 119ndash140 2010

[48] M S Berman ldquoA special law of variation for Hubblersquos parame-terrdquo Il Nuovo Cimento B vol 74 pp 182ndash186 1983

[49] V B Johri andK Desikan ldquoCosmological models with constantdeceleration parameter in Brans-Dicke theoryrdquoGeneral Relativ-ity and Gravitation vol 26 no 12 pp 1217ndash1232 1994

[50] J L Tonry B P Schmidt B Barris et al ldquoCosmological resultsfrom high-z supernovaerdquoThe Astrophysical Journal vol 594 p1 2003

[51] A Clocchiatti B P Schmidt and A V Filippenko ldquoHubbleSpace Telescope and Ground-based Observations of Type IaSupernovae at Redshift 05 Cosmological Implicationsrdquo TheAstrophysical Journal vol 642 no 1 2006

[52] C L Bennett R S Hill G Hinshaw et al ldquoFirst-yearWilkinson Microwave Anisotropy Probe (WMAP) observationsforeground emissionrdquo The Astrophysical Journal SupplementSeries vol 148 no 1 pp 97ndash117 2003

[53] M Tegmark M R Blanton M A Strauss et al ldquoThe three-dimensional power spectrum of galaxies from the sloan digitalsky surveyrdquoTheAstrophysical Journal vol 606 no 2 article 7022004

[54] J Frieman M Turner and D Huterer ldquoDark energy andthe accelerating universerdquo Annual Review of Astronomy andAstrophysics vol 46 pp 385ndash432 2008

Advances in High Energy Physics 9

[55] S del Campo C Fabris R Herrera and W Zimdahl ldquoHolo-graphic dark-energymodelsrdquo Physical Review D vol 83 ArticleID 123006 2011

[56] S del Campo R Herrera and D Pavon ldquoInteracting modelsmay be key to solve the cosmic coincidence problemrdquo Journalof Cosmology and Astroparticle Physics vol 2009 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

8 Advances in High Energy Physics

a cosmological constantrdquo The Astronomical Journal vol 116article 1009 1998

[18] A G Riess L-G Strolger J Tonry et al ldquoType Ia supernovadiscoveries at 119911 gt 1 from the Hubble Space Telescope evidencefor past deceleration and constraints on dark energy evolutionrdquoThe Astrophysical Journal vol 607 pp 665ndash687 2004

[19] S Permutter S Gabi G Goldhaber et al ldquoMeasurements ofthe cosmological parameters omega and lambda from the first7 supernovae at 119911 ge 035rdquoThe Astrophysical Journal vol 483 p565 1997

[20] S J Permutter G Aldering M Della Valle et al ldquoDiscovery ofa supernova explosion at half the age of the Universerdquo Naturevol 391 pp 51ndash54 1998

[21] S J Permutter G Aldering G Goldhaber et al ldquoMeasurementsofΩ and Λ from 42 High-Redshift SupernovaerdquoThe Astrophys-ical Journal vol 517 no 2 p 565 1999

[22] D N Spergel L Verde H V Peiris et al ldquoFirst-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations determi-nation of cosmological parametersrdquo The Astrophysical JournalSupplement Series vol 148 no 1 p 175 2003

[23] D N Spergel R Bean O Dore et al ldquoThree-year WilkinsonMicrowave Anisotropy Probe (WMAP) observations implica-tions for cosmologyrdquo The Astrophysical Journal SupplementSeries vol 170 no 2 article 377 2007

[24] R RCaldwell ldquoCosmicMicrowaveBackground and Supernovaconstraints on quintessence concordance regions and targetmodelsrdquo Physical Review D vol 69 2004

[25] R R Caldwell ldquoSudden gravitational transitionrdquo PhysicalReview D vol 73 2006

[26] A G Cohen D B Kaplan and A E Nelson ldquoEffective fieldtheory black holes and the cosmological constantrdquo PhysicalReview Letters vol 82 no 25 pp 4971ndash4974 1999

[27] E J Copeland M Sami and S Tsujikawa ldquoDynamics of darkenergyrdquo International Journal of Modern Physics vol 15 no 11pp 1753ndash1935 2006

[28] A Deo J S Alcaniz and D Jain ldquoCosmological consequencesof a chaplygin gas dark energyrdquo Physical Review D vol 67Article ID 023515 2004

[29] B Ratra and J Peebles ldquoFractal model for disordered magnetsrdquoPhysical Review D vol 37 p 321 1988

[30] R R Caldwell ldquoA phantom menace Cosmological conse-quences of a dark energy component with super-negativeequation of staterdquo Physics Letters B vol 545 no 1-2 pp 23ndash292002

[31] E Elizalde S Nojiri and S D Odinstov ldquoLate-time cosmologyin a (phantom) scalar-tensor theory dark energy and thecosmic speed-uprdquo Physical Review D vol 70 no 4 Article ID043539 2004

[32] A Kamenshchik U Moschella and V Pasquier ldquoAn alternativeto quintessencerdquo Physics Letters B vol 511 no 2-4 pp 265ndash2682001

[33] T Padmanabhan ldquoAccelerated expansion of the universe drivenby tachyonic matterrdquo Physical Review D vol 66 Article ID021301 2002

[34] D D Pawar Y S Solanke and S N Bayaskar ldquoKantowski-sachscosmological models with constat EoS parameter in BarberrsquosSecond Self Creation Theoryrdquo Prespacetime Journal vol 5 no2 pp 60ndash68 2014

[35] D D Pawar and Y S Solanke ldquoExact kantowski-sachsanisotropic dark energy cosmological models in brans dicke

theory of gravitationrdquo International Journal of TheoreticalPhysics vol 53 no 9 pp 3052ndash3065 2014

[36] L P Chimento ldquoExtended tachyon field Chaplygin gas andsolvable 119896-essence cosmologiesrdquo Physical Review D vol 69 no12 Article ID 123517 10 pages 2004

[37] C W Misner ldquoThe isotropy of the universerdquo The AstrophysicalJournal vol 151 p 431 1968

[38] K Land and J Maqueijo ldquoExamination of evidence for apreferred axis in the cosmic radiation anisotropyrdquo PhysicalReview Letters vol 95 Article ID 071301 2005

[39] M Demianski ldquoTilted plane symmetric magnetized cosmolog-ical modelsrdquo Physical Review D vol 46 no 4 pp 1391ndash13981992

[40] D D Pawar V D Dagwal and Y S Solanke ldquoTilted plane sym-metricmagnetized cosmological modelsrdquo Prespacetime Journalvol 5 no 2 pp 368ndash377 2014

[41] D D Pawar and V J Dagwal ldquoBianchi type IX string cos-mological model in general relativityrdquo International Journal ofTheoretical Physics vol 53 no 7 pp 2441ndash2450 2014

[42] R Bali and S Dave ldquoBianchi type IX string cosmological modelfor perfect fluid distribution in general relativityrdquo PramanaJournal of Physics vol 56 p 4 2001

[43] A Tyagi and K Sharma ldquoBianchi type IX string cosmologicalmodel for perfect fluid distribution in general relativityrdquoChinesePhysics Letters vol 27 no 7 Article ID 079801 2010

[44] V U M Rao and Y V S S Sanyasiraju ldquoExact Bianchi-typeVIII and IX models in the presence of zero-mass scalar fieldsrdquoAstrophysics and Space Science vol 187 no 1 pp 113ndash117 1992

[45] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 no 4 pp 689ndash6932013

[46] D D Pawar and V J Dagwal ldquoBianchi type IX two fluidscosmological models in general relativityrdquo International Journalof Scientific and Engineering Research vol 4 pp 689ndash693 2013

[47] O Akarsu and C B Kilinc ldquoLRS Bianchi type I models withanisotropic dark energy and constant deceleration parameterrdquoGeneral Relativity and Gravitation vol 42 pp 119ndash140 2010

[48] M S Berman ldquoA special law of variation for Hubblersquos parame-terrdquo Il Nuovo Cimento B vol 74 pp 182ndash186 1983

[49] V B Johri andK Desikan ldquoCosmological models with constantdeceleration parameter in Brans-Dicke theoryrdquoGeneral Relativ-ity and Gravitation vol 26 no 12 pp 1217ndash1232 1994

[50] J L Tonry B P Schmidt B Barris et al ldquoCosmological resultsfrom high-z supernovaerdquoThe Astrophysical Journal vol 594 p1 2003

[51] A Clocchiatti B P Schmidt and A V Filippenko ldquoHubbleSpace Telescope and Ground-based Observations of Type IaSupernovae at Redshift 05 Cosmological Implicationsrdquo TheAstrophysical Journal vol 642 no 1 2006

[52] C L Bennett R S Hill G Hinshaw et al ldquoFirst-yearWilkinson Microwave Anisotropy Probe (WMAP) observationsforeground emissionrdquo The Astrophysical Journal SupplementSeries vol 148 no 1 pp 97ndash117 2003

[53] M Tegmark M R Blanton M A Strauss et al ldquoThe three-dimensional power spectrum of galaxies from the sloan digitalsky surveyrdquoTheAstrophysical Journal vol 606 no 2 article 7022004

[54] J Frieman M Turner and D Huterer ldquoDark energy andthe accelerating universerdquo Annual Review of Astronomy andAstrophysics vol 46 pp 385ndash432 2008

Advances in High Energy Physics 9

[55] S del Campo C Fabris R Herrera and W Zimdahl ldquoHolo-graphic dark-energymodelsrdquo Physical Review D vol 83 ArticleID 123006 2011

[56] S del Campo R Herrera and D Pavon ldquoInteracting modelsmay be key to solve the cosmic coincidence problemrdquo Journalof Cosmology and Astroparticle Physics vol 2009 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Advances in High Energy Physics 9

[55] S del Campo C Fabris R Herrera and W Zimdahl ldquoHolo-graphic dark-energymodelsrdquo Physical Review D vol 83 ArticleID 123006 2011

[56] S del Campo R Herrera and D Pavon ldquoInteracting modelsmay be key to solve the cosmic coincidence problemrdquo Journalof Cosmology and Astroparticle Physics vol 2009 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FluidsJournal of

Atomic and Molecular Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Condensed Matter Physics

OpticsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstronomyAdvances in

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Superconductivity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Statistical MechanicsInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GravityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AstrophysicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Physics Research International

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solid State PhysicsJournal of

 Computational  Methods in Physics

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PhotonicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Biophysics

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ThermodynamicsJournal of