cosmology with cmb anisotropy

Cosmology Cosmology with CMB with CMB

anisotropyanisotropyTarun Souradeep

I.U.C.A.A, Pune

WHEPP-9 (Jan 10, 2005)

The Isotropic Universe

Serendipitous discovery of the dominant Radiation content of the universe as an extremely isotropic, Black-body bath at temperature

TT00=2.725=2.725§§0.0020.002K .K .

““Clinching support for Hot Big Bang model”Clinching support for Hot Big Bang model”

The dominant radiation component in the universe

(D. Scott ’99)

~ 400 CMB photons per cubic cm.

The most perfect Black-Body spectrum in nature

COBE website

COBE –FIRAS

The CMB temperature –A single number

characterizes the radiation content of the universe!!

(figs: Bond, 1996)

COBE-FIRAS results strongly constrain any Energy input into the CMB in the not-so-early universe

)5000500(

4 ,105.2m

EE

10 Ghz30Ghz

60 Ghz 600 Ghz

ARCADE 2004

After 25 years of intense search, tiny variations (~10 p.p.m.) of CMB temperature sky map finally discovered.

“Holy grail of structure formation”

Predicted as precursors to the observed large scale structure

The Perturbed Universe The Isotropic Universe

Cosmic Microwave Background – a probe beyond the cosmic horizon

Pre-recombination : Tightly coupled to, and in thermal equilibrium with, ionized matter.

Post-recombination :Freely propagating through (weakly perturbed) homogeneous & isotropic cosmos.

Pristine relic of a hot, dense & smooth early universe - Hot Big Bang model

CMB anisotropy is related to the tiny primordial fluctuations which formed the Large scale Structure through gravitational instability

Simple linear physics allows for accurate predictions

Consequently a powerful cosmological probe

0H

DM

b

tot

Mildly Perturbed universe at z=1100

Present universe at z=0

Gravitational Instability

Cosmic matter content

Baryonic

matter

Dark matter

Expansion rate

Dark energy

Cosmic age

Multi-parameter (7-11) joint estimation (complex covariance, degeneracies, priors,… marginal distributions) Strategies to search & Locate best parameters: Markov Chain Monte Carlo

Cosmological Parameters

Optical depth

Fig.:R.Sinha, TS

),(),(2

l

l

lmlmlmYaT

CMB Anisotropy Sky map => Spherical Harmonic decomposition

Statistics of CMB

Statistical isotropy

*' ' ' 'lm l m l ll mma a C

Gaussian CMB anisotropy completely specified by theangular power spectrumangular power spectrum IF

(=> Correlation function C(n,n’)=hT Ti is rotationally invariant)

The Angular power spectrum of CMB anisotropy is considered a powerful tool for constraining cosmological parameters.

Fig. M. White 1997

The Angular power spectrum of the CMB anisotropy dependssensitively on the present matter current of the universe and the spectrum of primordial perturbations

lC

•Low multipole : Sachs-Wolfe plateau

• Moderate multipole : Acoustic “Doppler” peaks

• High multipole : Damping tail

CMB physics is verywell understood !!!

Fig:Hu & Dodelson 2002

Sensitive to curvature

K1220l

l

Fig:Hu & Dodelson 2002

Sensitive to Baryon density

KT 74

Boomerang 1998

DASI 2002 (Degree Angular scale

Interferometer) Archeops 2002

Python-V 1999, 2003

Post-COBE Ground & Balloon Experiments

Highlights of CMB Anisotropy Measurements (1992- 2002)

First year data results announced on Feb. 11,

2003 !

NASA Launched July 2001

Wilkinson Microwave Anisotropy Probe

30% sky daily, Whole sky every 6 months

NASA/WMAP science team

K band 23 GHz (1 DA)

Ka band 33 GHz (1 DA)

Q band 41 GHz (2 DA)

V band 61 GHz (2 DA)

W band 94 GHz (4 DA)

CMB anisotropy signal

10 independent Difference assemblies over 5 frequencies

dus saal baad ….


650for 1 Noise / Signal

350for errors limited varianceCosmic

IIT Kanpur + IUCAA

Saha, Jain,Souradeep 2005(astro-ph/0508383)

Independent, self contained analysis of WMAP multi-frequency maps Only input : CMB anisotropy is achromatic (frequency independent)No extraneous foreground info. ! I.e., free of uncertainty of foreground modeling

Black: IITK+IUCAA

Red : WMAP team

Controlling other SystematicsEg.,Non-circular beam effect in CMB

measurements

(S. Mitra, A. Sengupta, Souradeep, PRD 2004)WMAP Q beam Eccentricity =0.7

Close to the corrections expected in

the WMAP 2nd data release

(74.40.3, 220.80.8)(74.7 0.5, 220.1 0.8)

(49.6 1.2, 545 17)(48.8 0.9, 546 10)

(42.2 0.9, 418.7 5.5) (41.0 0.5, 411.7 3.5)

Saha, Jain,Souradeep 2005(astro-ph/0508383)

Power spectrum of mass distribution

( Tegmark et al. 2004)

(Fig: Tegmark)CMB+LSS

(WMAP+SDSS analysis: Tegmark et al. 2004)

CMB Task force report 2005

Near future : High resolution Cl (SPT)

0H

DM

b

tot

Mildly Perturbed universe at z=1100

Present universe at z=0

Gravitational Instability

Cosmic matter content

SLOAN DIGITAL SKY SURVEY (SDSS)

Few Gpc.

Present distribution of matter

One little telltale bump !! A small excess in correlation at 150

Mpc.!SDSS survey

(astro-ph/0501171)

150 Mpc.

(Einsentein et al. 2005)

1 2( ) ( ) ( )r r r

Acoustic Baryon oscillations!!

150 Mpc.


2-po

int c

o rre

latio

n of

de

nsi ty

con

tra s

t Acoustic Baryon oscillations in the matter

correlation function !!

The same CMB oscillations at

low redshifts !!!SDSS survey

(astro-ph/0501171)

Strong evidence ofGravitational instability mechanism

for structure formation (from adiabatic initial perturbations) !!!

150 Mpc.


105 h-1 ¼ 150

Quantum fluctuations

super adiabatic amplified by

inflation (rapid expansion)

Galaxy & Large scale

Structure formation

Via gravitational instability

Early Universe

Present Universe

The Cosmic screen

PARAMETERS OF THE

INITIAL CONDITIONS

FROM EARLY UNIVERSE

COSMOLOGICAL

PARAMETERS

Power spectrum‘Nearly’ Scale invariant /scale free form

( for the Geometry & Topology of the universe)

Spin characteristics Scalar --- Density perturbations

Tensor --- Gravity waves

Vector --- rotational modes Type of scalar perturbations

Adiabatic --- no entropy fluctuations

Isocurvature -- no curvature fluctuations

Underlying statistics Gaussian

Non-Gaussian

The nature of initial/primordial perturbations

Thompson scattering of the CMB anisotropy quadrupole at the surface of last scattering generates a linear polarization pattern in the CMB.

Three additional Power spectra (ClTT +.. ):

• two polarization modes (ClEE , Cl

BB )

• cross correlation with temperature anisotropy ClTE .

Initial metric perturbation mix correspondence :

Scalar perturbations predominantly generate the Electric (E) polarization mode.

Vector perturbations predominantly generate the magnetic (B) polarization mode .

Tensor perturbations generate the both modes in comparable amounts . Temperature anisotropy Cross-correlation only with the E-mode.

(Fig:Hu & White , 97)

First detection by DASI (2002)

l =220-400

Regularly updated Sept 2004: CBI, DASI,CAPMAP

July 2005: Boomerang

ClEE

ClTE

ClTT


Proof of inflation?Anti-correlation peak

KT 35,9137

10920

reionz

20for with Consistent T

Adiabatic ICTE peak out of

phase 300

(MacTavish et al. astro-ph/0507503)

Out of phase location of peaks in EE, TE relative to TT implies adiabatic initial perturbations!!!

Null BB: Awaiting direct signature of tensor perturbations, a.k.a. gravity waves !!!


BUT, please read the fine print !Data combos, priors, parameterization

BUT, please read the fine print !Data combos, priors, parameterization,…


K=-0.037§0.04

The curvature (density) of the Universe

K=-0.027§0.016K=-0.022§0.017


m < 0.16 eV

3- degenerate mass

= 3 m /(94.0 eV)

f= /DM

m < 0.4 eVm < 1.0 eV

(95% CL)

Cosmological constraints on mass


w=-0.94§0.1

w=-0.86§0.4

Constant equation of state,

w

The nature of dark energy


AT/AS < 0.71

AT/AS < 0.36

Tensor to scalar ratio

Tensor to scalar ratio is a crucial discriminant of EU scenarios

Courtesy: A. Coorey (EPIC)

10-3 : reasonable low end of inflationary

possibilities

Early Universe

Present Universe

The Cosmic screen

PARAMETERS OF THE

INITIAL CONDITIONS

FROM EARLY UNIVERSE

COSMOLOGICAL

PARAMETERS

CMB anisotropy has two independent aspects:

( ) ( )l P kdkC Gk

k

( )P k ( )lG kPost recombination Radiation transport in a given cosmology

Primordial power spectrum from Early universe

(Tegmark & Zaldariagga 97, Gawaiser & Silk ’00, Matsumiya et al. ’02..)


)74102 (COBE

2 282 Quadrupole Low

KT

KT

Suppression of power on low multipoles (l=2,3)

(Shafieloo & Souradeep, 2004 PRD )

Improved Error sensitive iterative Richardson-Lucy deconvolution method

)()( kGkPk

dkC ll

Primordial power spectrum from Early universe can deconvolved from CMB anisotropyspectrum

Recovered spectrum shows an infra-red cut-off on Horizon scale !!! Is it cosmic topology ? Signature of pre-inflationary phase ? New physics ? ….

Recovering the primordial power spectrum

Horizon scale

0.68

0.71

0.75

0.040

0.044

0.048

0.31

0.27

0.23

Wavelet Decomposition of features(TS+ Rangarajan, Panigrahi, Manimaran: in progress)

Infrared cutoff

Superimposed Oscillations

Recovery of the primordial power spectrum

(Tocchini-Vaentini, Hoffman, Silk astro-ph/0509478)

A reconfirmation of our results using different deconvolution method !

Two independent aspects of CMB anisotropy :

( )

( )

( )

( )

( )

( )

( ) ( )

TT TT

EE

B

EE

B B

T

B

ETE

dkCkdkCk

dkC

G k

G k

G k

P k

P k

P

G k

k

P k

kdkCk

( ), ( ), ( )S T isoP k P k P k ( ), ( ), ( ), ( )TT EE BB TEG k G k G k G k

Primordial power spectra from Early universe

Post recombination Radiative transport kernels in a given cosmology

Absence of large scale power


Intriguing lack of correlations at large angular scales ( ¸ 60±)

Can imply more than just

the suppression of power in the

low multipoles !

Asymmetries in the CMB anisotropy

Broadly, statistical properties are not invariant under rotations

I.e., Breakdown of Statistical Isotropy ?

N-S asymmetry Eriksen, et al. 2004, Hansen et al. 2004 (in local power)Larson & Wandelt 2004, Park 2004 (genus stat.)

Special directions “Axis of Evil”Tegmark et al. 2004 (l=2,3 aligned)Copi et al. 2004 (multipole vectors)Land & Magueijo 2004 (cubic anomalies)Prunet et al., 2004 (mode coupling)

Underlying `template’ pattern Jaffe et al. 2005 (Bianchi VIIh:mild cosmic rotation?)..

High N-S asymmetry

Low N-S asymmetry

Fig: H. K. Eriksen, et al. 2003

WMAP first year data

Bianchi template

Difference map

Possibilities:• Statistically Isotropic, Gaussian models• Statistically Isotropic, non-Gaussian models• Statistically An-isotropic, Gaussian models• Statistically An-isotropic, non-Gaussian models

Statistics of CMB

1 2 1 2ˆ ˆ ˆ ˆ( , ) ( )C n n C n n

*' ' ' 'lm l m l ll mma a C

Sources of Statistical AnisotropySources of Statistical Anisotropy• Ultra large scale structure and cosmic topology.

• Anisotropic cosmology• Primordial magnetic fields (based on Durrer et al. 98, Chen et al. 04)

• Observational artifacts: – Anisotropic noise – Non-circular beam – Incomplete/unequal sky coverage – Residuals from foreground removal

Can we measure correlation patterns?the COSMIC CATCH is

Beautiful Correlation patterns could underlie the CMB tapestry Figs. J. Levin

1 2 1 2ˆ ˆ ˆ ˆ( , ) ( )C n n C n n

2

21221)ˆ,ˆ()(

81

nnCdndnd

Bipolar Power spectrum (BiPS) :Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical AnisotropyA Generic Measure of Statistical Anisotropy

A A weighted averageweighted average of the of the correlation function over all correlation function over all

rotationsrotations

)ˆ,ˆ(8

1)ˆˆ( :Recall 21221 nnCdnnC Bipolar multipole index

Wigner Wigner rotation rotation matrixmatrix

)()(

mmmD

Characteristic Characteristic functionfunction

Hajian & Souradeep ApJ. Lett 2003

Hajian, Souradeep & Cornish ApJ. Lett. 2005

2

22122

)](8

1[)ˆ,ˆ()12(21

dnnCdd nn

0)(

d

Statistical IsotropyStatistical Isotropy

Correlation is invariant under rotations

)ˆ,ˆ()ˆ,ˆ( 2121 nnCnnC

00

• Correlation is a two point function on a sphere

• Inverse-transform )()(

)}()({21

21

2211

21

2121

21

nYnYCnYnY

mlmlmm

LMmmll

LMll

LMllLMll

LMll nYnYAnnC )}()({),( 2121 21

21

21

LM

mmmlml

LMllnnLMll

mlmlCaa

nYnYnnCddA

221121

2211

212121*

2121 )}()(){,(

BiPS: In Harmonic SpaceBiPS: In Harmonic Space

BiPoSH

Linear combination of off-diagonal elements

Bipolar spherical harmonics.

Clebsch-Gordan

0||21

21,,

2 llM

MllABiPS:BiPS:

rotationally invariantrotationally invariant

M

mmMlml

Mll mMlml

CaaA

12111

121121

* BiPoSH BiPoSH

coefficients :coefficients :• Complete,Independent linear combinations of off-diagonal correlations.• Encompasses other specific measures of off-diagonal terms, such as

- Durrer et al. ’98 :- Prunet et al. ’04 :

M

Mmliml

Mllimllm

il CAaaD

1'1

)(

M

Mmlml

Mllmllml CAaaD

2'2

Recall: Coupling of angular momentum states Mmlml |2211 0, 21121 Mmmlll

''*

'' : violationSI mmlllmllm Caa

Radical breakdown

**''''

*''

lmlmmlml

mllm

aaaa

aa

(Bond, Pogosyan & Souradeep 1998, 2002)

MllA2

'

MllA4

'

Understanding BiPoSH coefficients

*' ' ' '

SI violation

:

lm l m l ll mma a C

' '''

'

Measure cross correlation in

lml m

LMlm lm

mm

LM

lm

ll a a CA

a

Bipolar spherical harmonics

Spherical Harmonic coefficents

BiPoSH coefficents

Angular power spectrum

BiPS

lma MllA

'

lC

Spherical harmonics


Bipolar spherical harmonics

Spherical Harmonic Transforms

BipoSH Transforms

Angular power spectrum

BiPS(Bipolar Power

Spectrum)

lma MllA

'

lC

Spherical harmonics


Measure of Statistical IsotropyMeasure of Statistical Isotropy

00

isotropy Stat.

2

''

'''

' ''

BA

CaaA

Mll

Mll

Mmllm

mm

Mll mlml

• Averaging over l,l’& M beats down Cosmic variance .• Fast: Advantage of fast SH transform. (1 min. /alpha 1.25 GHz proc.: Healpix 512, BiPS upto 20 )

• Orientation independent.

bias

SH transform of the map

Statistical Isotropy of CMB Statistical Isotropy of CMB AnisotropyAnisotropy

W(l)

WMAP CMB anisotropy map

WMAP Angular power spectrum

WMAP Bipolar power spectrum (BiPS)

Fig: NASA/WMAP science team

Fig: NASA/WMAP science team

Hajian & Souradeep ApJ. Lett 2003

Hajian, Souradeep & Cornish ApJ. Lett. 2005

BiPS implyWMAP is Statistically

Isotropic !!

Cosmology with CMB anisotropy• Precise values of the parameters of the ‘working model’ of

cosmology.

• Direct evidence of gravitational instability being responsible for structure formation.

• Initial/primordial perturbations from (simple) inflation– adiabatic density perturbations – Gaussian random fields – A non-zero tensor component ? (cosmic gravity wave background )

• Observable signatures of Ultra-large structure of the cosmos, or, new physics in early universe– infra-red cutoff & feature in the primordial power spectrum – Violation of statistical isotropy : Are Cl adequate descriptor of CMB ?

(Detection of cosmic topology ? Is the universe observably finite ?)

Thank Thank you !!!you !!!


cosmology with cmb anisotropy

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