dark energy from variation of the fundamental scale
DESCRIPTION
Dark Energy from variation of the fundamental scale. What is our universe made of ?. fire , air, water, soil !. quintessence !. Dark Energy dominates the Universe. Energy - density in the Universe = Matter + Dark Energy 25 % + 75 %. Matter : Everything that clumps. - PowerPoint PPT PresentationTRANSCRIPT
Dark Energy Dark Energy from variation of thefrom variation of thefundamental scalefundamental scale
What is our universe What is our universe made of ?made of ?
quintessence !fire , air,
water, soil !
Dark Energy Dark Energy dominates the Universedominates the Universe
Energy - density in the Energy - density in the UniverseUniverse
==
Matter + Dark EnergyMatter + Dark Energy
25 % + 75 %25 % + 75 %
Abell 2255 Cluster~300 Mpc
Matter : Everything that clumpsMatter : Everything that clumps
Dark Energy density isDark Energy density isthe same at every point of the same at every point of
space space
“ homogeneous “ “ homogeneous “
No local force –No local force –“ In what direction should it “ In what direction should it
draw ? “draw ? “
What is Dark Energy ?
Cosmological Constant or Quintessence ?
Quintessence and Quintessence and solution of solution of
cosmological constant cosmological constant problem should be problem should be
related !related !
Cosmological ConstantCosmological Constant- Einstein -- Einstein -
Constant Constant λλ compatible with all compatible with all symmetriessymmetries
No time variation in contribution to No time variation in contribution to energy densityenergy density
Why so small ? Why so small ? λλ/M/M44 = 10 = 10-120-120
Why important just today ?Why important just today ?
Cosm. Const. | Quintessence static | dynamical
challengechallenge
explain why Dark Energy explain why Dark Energy goes to zero asymptotically , goes to zero asymptotically ,
not to a constant !not to a constant !
ΩΩmm + X = 1 + X = 1
ΩΩmm : 25% : 25%
ΩΩhh : 75% : 75% Dark EnergyDark Energy
?
Time dependent Dark Time dependent Dark Energy :Energy :
QuintessenceQuintessence What changes in time ?What changes in time ?
Only dimensionless ratios of mass scales Only dimensionless ratios of mass scales are observable !are observable !
V : potential energy of scalar field or cosmological V : potential energy of scalar field or cosmological constantconstant
V/MV/M4 4 is observableis observable
Imagine the Planck mass M increases …Imagine the Planck mass M increases …
Fundamental mass scaleFundamental mass scale
Unification fixes parameters with Unification fixes parameters with dimensionsdimensions
Special relativity : cSpecial relativity : c Quantum theory : hQuantum theory : h Unification with gravity : Unification with gravity :
fundamental mass scalefundamental mass scale ( Planck mass , string tension , …)( Planck mass , string tension , …)
Fundamental mass scaleFundamental mass scale
Fixed parameter or dynamical Fixed parameter or dynamical scale ?scale ?
Dynamical scale FieldDynamical scale Field Dynamical scale compared to Dynamical scale compared to
what ?what ?
momentum versus mass momentum versus mass
( or other parameter with ( or other parameter with dimension )dimension )
Cosmon and Cosmon and fundamental mass scalefundamental mass scale
Assume all mass parameters are Assume all mass parameters are proportional to scalar field proportional to scalar field χχ (GUTs, (GUTs, superstrings,…)superstrings,…)
MMpp~ ~ χχ , m , mprotonproton~ ~ χχ , , ΛΛQCDQCD~ ~ χχ , M , MWW~ ~ χχ ,… ,…
χχ may evolve with time : may evolve with time : cosmoncosmon mmnn/M : ( almost ) constant - /M : ( almost ) constant - observationobservation !!
Only ratios of mass scales are Only ratios of mass scales are observableobservable
Example :Example :
Field Field χχ is connected to scale of transition is connected to scale of transitionfrom higher dimensional physicsfrom higher dimensional physicsto effective four dimensional descriptionto effective four dimensional descriptionin theory without fundamental mass parameterin theory without fundamental mass parameter
(except for running of dimensionless couplings…)(except for running of dimensionless couplings…)
theory without explicit theory without explicit mass scalemass scale
Lagrange density:Lagrange density:
realistic theoryrealistic theory
χχ has no gauge interactions has no gauge interactions χχ is effective scalar field after is effective scalar field after
“integrating out” all other scalar “integrating out” all other scalar fieldsfields
Dilatation symmetryDilatation symmetry Lagrange density:Lagrange density:
Dilatation symmetry forDilatation symmetry for
Conformal symmetry for Conformal symmetry for δδ=0=0
Dilatation anomalyDilatation anomaly
Quantum fluctuations responsible forQuantum fluctuations responsible for
dilatation anomalydilatation anomaly Running couplings:Running couplings: hypothesishypothesis
Renormalization scale Renormalization scale μμ : ( momentum : ( momentum scale )scale )
λλ~(~(χχ//μμ) ) –A–A
E > 0 : crossover QuintessenceE > 0 : crossover Quintessence
Asymptotic behavior of Asymptotic behavior of effective potentialeffective potential
λλ ~ ( ~ (χχ//μμ) ) –A–A
V ~ (V ~ (χχ//μμ) ) –A –A χχ44
VV ~ ~ χχ 4–A 4–A
crucial : behavior for large χ !crucial : behavior for large χ !
Dilatation anomaly and Dilatation anomaly and quantum fluctuationsquantum fluctuations
Computation of running couplings Computation of running couplings ( beta functions ) needs unified theory !( beta functions ) needs unified theory !
Dominant contribution from modes Dominant contribution from modes with momenta ~with momenta ~χχ ! !
No prejudice on “natural value “ of No prejudice on “natural value “ of anomalous dimension should be anomalous dimension should be inferred from tiny contributions at inferred from tiny contributions at QCD- momentum scale !QCD- momentum scale !
Asymptotic behavior of Asymptotic behavior of effective potentialeffective potential
VV ~ ~ χχ 4–A 4–A
e.g. Ve.g. V ~ ~ χχ 2 2 or V or V ~ ~ const.const.
crucial : behavior for large χ !crucial : behavior for large χ !
CosmologyCosmology
Cosmology : Cosmology : χχ increases with time ! increases with time !
( due to coupling of ( due to coupling of χχ to curvature scalar to curvature scalar ))
for large for large χχ the ratio V/M the ratio V/M4 4 decreases to decreases to zerozero
Effective cosmological constant vanishes Effective cosmological constant vanishes asymptotically for large t !asymptotically for large t !
Asymptotically vanishing Asymptotically vanishing effective “cosmological effective “cosmological
constant”constant”
Effective cosmological constant ~ V/MEffective cosmological constant ~ V/M4 4
λλ ~ ( ~ (χχ//μμ) ) –A–A
V ~ (V ~ (χχ//μμ) ) –A –A χχ44
M = M = χχ
V/MV/M4 4 ~(~(χχ//μμ) ) –A –A
Weyl scalingWeyl scaling
Weyl scaling : gWeyl scaling : gμνμν→→ (M/ (M/χχ))2 2 ggμνμν , ,
φφ/M = ln (/M = ln (χχ 44/V(/V(χχ))))
Exponential potential : V = MExponential potential : V = M44 exp(- exp(-φφ/M)/M)
No additional constant !No additional constant !
Without dilatation – anomaly :V= const. Massless Goldstone boson = dilaton
Dilatation – anomaly :V (φ )Scalar with tiny time dependent mass : cosmon
quantum fluctuations and quantum fluctuations and naturalnessnaturalness
Jordan- and Einstein frame completely Jordan- and Einstein frame completely equivalent on level of effective action equivalent on level of effective action and field equations ( and field equations ( afterafter computation computation of quantum fluctuations ! )of quantum fluctuations ! )
Treatment of quantum fluctuations Treatment of quantum fluctuations depends on frame : Jacobian for depends on frame : Jacobian for variable transformation in functional variable transformation in functional integralintegral
What is natural in one frame may look What is natural in one frame may look unnatural in another frameunnatural in another frame
quantum fluctuations quantum fluctuations and framesand frames
Einstein frame : quantum fluctuations Einstein frame : quantum fluctuations make zero cosmological constant look make zero cosmological constant look unnaturalunnatural
Jordan frame : quantum fluctuations Jordan frame : quantum fluctuations are at the origin of dilatation anomaly;are at the origin of dilatation anomaly;
key ingredient for key ingredient for solutionsolution of of cosmological constant problem !cosmological constant problem !
fixed points and fluctuation fixed points and fluctuation contributions of individual contributions of individual
componentscomponents
If running couplings influenced by fixed points:If running couplings influenced by fixed points:individual fluctuation contribution can be huge individual fluctuation contribution can be huge
overestimate !overestimate !
here : fixed point at vanishing quartic coupling and here : fixed point at vanishing quartic coupling and anomalous dimension anomalous dimension VV ~ ~ χχ 4–A 4–A
it makes no sense to use naïve scaling argument to it makes no sense to use naïve scaling argument to infer individual contribution infer individual contribution VV ~ h ~ h χχ 4 4
Exponential cosmon Exponential cosmon potentialpotential
Exponential potential : Exponential potential : V = MV = M44 exp(- exp(-φφ/M)/M)
Cosmic AttractorsCosmic Attractors
Solutions independent of initial conditions
typically V~t -2
φ ~ ln ( t )
Ωh ~ const.
details depend on V(φ)or kinetic term
early cosmology
partial solution of partial solution of cosmological constant cosmological constant
problemproblem
Ωh ~ const.
Dark Energy and Matter of similar size !
Cosmological mass scalesCosmological mass scales Energy densityEnergy density
ρρ ~ ( 2.4×10 ~ ( 2.4×10 -3-3 eV )eV )- 4- 4
Reduced Planck Reduced Planck massmass
M=2.44M=2.44×10×101818GeVGeV Newton’s constantNewton’s constant
GGNN=(8=(8ππM²)M²)
Only ratios of mass scales are observable !Only ratios of mass scales are observable !
homogeneous dark energy: homogeneous dark energy: ρρhh/M/M44 = 6.5 = 6.5 10ˉ¹²¹10ˉ¹²¹
matter: matter: ρρmm/M/M4= 3.5 10ˉ¹²¹= 3.5 10ˉ¹²¹
Time evolutionTime evolution
ρρmm/M/M4 4 ~ aˉ~ aˉ³ ³ ~~
ρρrr/M/M4 4 ~ aˉ~ aˉ44 ~ ~ t t -2-2 radiation dominated universeradiation dominated universe
Huge age small ratioHuge age small ratio
Same explanation for small dark Same explanation for small dark energy?energy?
tˉ² matter dominated universe
tˉ3/2 radiation dominated universe
QuintessenceQuintessenceDynamical dark energy ,Dynamical dark energy , generated by scalargenerated by scalar fieldfield
(cosmon)(cosmon)
C.Wetterich,Nucl.Phys.B302(1988)668, C.Wetterich,Nucl.Phys.B302(1988)668, 24.9.87 24.9.87P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)LP.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, 20.10.8717, 20.10.87
Prediction :Prediction :
homogeneous dark energy homogeneous dark energyinfluences recent cosmologyinfluences recent cosmology
- of same order as dark - of same order as dark matter -matter -
Original models do not fit the present observationsOriginal models do not fit the present observations……. modifications. modifications
realistic quintessencerealistic quintessence
fraction in dark energy has fraction in dark energy has to to
increase in “recent time” !increase in “recent time” !
Crossover QuintessenceCrossover Quintessence
( like QCD gauge ( like QCD gauge coupling)coupling)
critical critical χχ where where δδ grows large grows largecritical critical φφ where k grows large k where k grows large k²²((φφ )= )=δδ((χχ)/4 )/4
kk²²((φφ )= “1/(2E( )= “1/(2E(φφcc – – φφ)/M)”)/M)”
ifif cc≈ 276/M ( tuning ! ) :≈ 276/M ( tuning ! ) : this will be responsible for relative increase of dark this will be responsible for relative increase of dark
energy in energy in presentpresent cosmological epoch cosmological epoch
Realistic cosmologyRealistic cosmology
Hypothesis on running Hypothesis on running couplings couplings
yields realistic cosmology yields realistic cosmology
for suitable values of A , E , for suitable values of A , E , φφcc
Quintessence becomes Quintessence becomes important “today”important “today”
many models…many models…
the quintessence of the quintessence of QuintessenceQuintessence
Cosmon – Field Cosmon – Field φφ(x,y,z,t)(x,y,z,t) similar to electric field , but no direction similar to electric field , but no direction ( scalar field )( scalar field )
may be fundamental or composite may be fundamental or composite (effective) field(effective) fieldHomogeneous und isotropic Universe : Homogeneous und isotropic Universe :
φφ(x,y,z,t)=(x,y,z,t)=φφ(t)(t)
Potential und kinetic energy of the cosmon Potential und kinetic energy of the cosmon -field-field
contribute to a dynamical energy density of contribute to a dynamical energy density of the Universe ! the Universe !
CosmonCosmon Scalar field changes its value even Scalar field changes its value even
in the in the present present cosmological epochcosmological epoch Potential und kinetic energy of Potential und kinetic energy of
cosmon contribute to the energy cosmon contribute to the energy density of the Universedensity of the Universe
Time - variable dark energy : Time - variable dark energy :
ρρhh(t) decreases with time !(t) decreases with time !
CosmonCosmon Tiny ( time varying ) massTiny ( time varying ) mass
mmcc ~ H ~ H
New long - range interactionNew long - range interaction
““Fundamental” Fundamental” InteractionsInteractions
Strong, electromagnetic, weakinteractions
gravitation cosmodynamics
On astronomical length scales:
graviton
+
cosmon
Dynamics of Dynamics of quintessencequintessence
Cosmon Cosmon : scalar singlet field: scalar singlet field
Lagrange density L = V + Lagrange density L = V + ½ ½ k(k(φφ)) (units: reduced Planck mass M=1)(units: reduced Planck mass M=1)
Potential : V=exp[-Potential : V=exp[-
““Natural initial value” in Planck era Natural initial value” in Planck era
today: today: =276=276
kinetialkinetial
Small almost constant k :Small almost constant k : Small almost constant Small almost constant ΩΩhh
Large k :Large k : Cosmon dominated universe ( like Cosmon dominated universe ( like
inflation )inflation )
Why has quintessence Why has quintessence become important “now” ?become important “now” ?
Doran,…Doran,…
coincidence problemcoincidence problem
What is responsible for increase of What is responsible for increase of ΩΩhh for z < 10 ? for z < 10 ?
a) Properties of cosmon a) Properties of cosmon potential or kinetic termpotential or kinetic term
Early quintessenceEarly quintessence ΩΩhh changes only changes only
modestlymodestly w changes in timew changes in time
transitiontransition special feature in special feature in
cosmon potential or cosmon potential or kinetic term becomes kinetic term becomes important “now”important “now”
tuning at ‰ leveltuning at ‰ level
Late quintessenceLate quintessence w close to -1w close to -1 ΩΩhh negligible in negligible in
early cosmologyearly cosmology
needs tiny needs tiny parameter, similar parameter, similar to cosmological to cosmological constantconstant
attractor solutionsattractor solutionsSmall almost constant k :Small almost constant k : Small almost constant Small almost constant ΩΩhh
This can explain tiny value of Dark This can explain tiny value of Dark Energy !Energy !
Large k :Large k : Cosmon dominated universe ( like Cosmon dominated universe ( like
inflation )inflation )
Transition to Transition to cosmon dominated universecosmon dominated universe
Large value k >> 1 : universe is Large value k >> 1 : universe is dominated by scalar fielddominated by scalar field
k increases rapidly : evolution of k increases rapidly : evolution of scalar fied essentially stopsscalar fied essentially stops
Realistic and natural quintessence: Realistic and natural quintessence:
k changes from small to large values k changes from small to large values after structure formationafter structure formation
b) Quintessence reacts to b) Quintessence reacts to some special event in some special event in
cosmologycosmology Onset of Onset of matter matter
dominancedominance
K- essenceK- essence Amendariz-Picon, Amendariz-Picon,
Mukhanov,Mukhanov, SteinhardtSteinhardt
needs higher needs higher derivativederivative
kinetic termkinetic term
Appearance of Appearance of non-linear non-linear
structurestructure
Back-reaction effectBack-reaction effect
needs coupling needs coupling betweenbetween
Dark Matter and Dark Matter and Dark EnergyDark Energy
Back-reaction effectBack-reaction effect
Needs large Needs large inhomogeneities inhomogeneities after structure has after structure has been formedbeen formed
Local cosmon field Local cosmon field participates in participates in structurestructure
Time dependence of dark Time dependence of dark energyenergy
cosmological constant : Ωh ~ t² ~ (1+z)-3
M.Doran,…
Early Dark EnergyEarly Dark Energy
early dark energyearly dark energy
expected in models expected in models
which explain same order ofwhich explain same order of
magnitude of magnitude of
dark energy and matter dark energy and matter naturallynaturally
effects of early dark effects of early dark energyenergy
modifies cosmological evolution (CMB)modifies cosmological evolution (CMB) slows down the growth of structureslows down the growth of structure
Early quintessence slows down Early quintessence slows down the the
growth of structuregrowth of structure
Growth of density Growth of density fluctuationsfluctuations
Matter dominated universe with Matter dominated universe with constantconstant ΩΩh h ::
Dark energy slows down structure Dark energy slows down structure formationformation
ΩΩh h < 10% during structure < 10% during structure formationformation
P.Ferreira,M.JoyceP.Ferreira,M.Joyce
bounds on bounds on Early Dark EnergyEarly Dark Energyafter WMAP’06after WMAP’06
G.Robbers,M.Doran,…G.Robbers,M.Doran,…
interpolation of interpolation of ΩΩhh
Cluster number relative to ΛCDM Two models
with 4% Dark Energy during structure formation
Fixed σ8
( normalization dependence ! )
Little Early Dark Energy can make Little Early Dark Energy can make large effect !large effect !
Non – linear enhancementNon – linear enhancement
More clusters at high redshift !
Bartelmann,Doran,…Bartelmann,Doran,…
work with J. Schwindtwork with J. Schwindt
hep-th/0501049hep-th/0501049
Quintessence from Quintessence from higher dimensionshigher dimensions
- an instructive - an instructive example -example -
Time varying constantsTime varying constants
It is not difficult to obtain It is not difficult to obtain quintessence potentials from higher quintessence potentials from higher dimensional or string theoriesdimensional or string theories
Exponential form rather generic Exponential form rather generic
( after Weyl scaling)( after Weyl scaling) But most models show too strong But most models show too strong
time dependence of constants !time dependence of constants !
Quintessence Quintessence from higher dimensionsfrom higher dimensions
An instructive example:An instructive example:
Einstein – Maxwell theory in six Einstein – Maxwell theory in six dimensionsdimensions
Warning : not scale - free !Warning : not scale - free !Dilatation anomaly replaced by explicit mass scales.Dilatation anomaly replaced by explicit mass scales.
Field equationsField equations
Energy momentum Energy momentum tensortensor
MetricMetricAnsatz with particular metric ( not Ansatz with particular metric ( not
most general ! )most general ! )which is consistent withwhich is consistent with
d=4 homogeneous and isotropic d=4 homogeneous and isotropic UniverseUniverse
and internal and internal U(1) x ZU(1) x Z22 isometry isometry
B ≠ 1 : football shaped internal geometryB ≠ 1 : football shaped internal geometry
Exact solutionExact solution
m : monopole number ( integer)m : monopole number ( integer)
cosmology with scalarcosmology with scalar
and potential V :and potential V :
Free integration Free integration constantsconstants
M , B , M , B , ΦΦ(t=0) , (d(t=0) , (dΦΦ/dt)(t=0) : continuous/dt)(t=0) : continuous
m : discretem : discrete
Conical singularitiesConical singularities
deficit angledeficit angle
singularities can be included with singularities can be included with energy momentum tensor on braneenergy momentum tensor on brane
bulk point of view : bulk point of view : describe everything in terms of bulk geometry describe everything in terms of bulk geometry ( not possible for modes on brane without tail ( not possible for modes on brane without tail
in bulk )in bulk )
Warped branesWarped branes
model is similar to first co-dimension model is similar to first co-dimension two brane model : C.W. two brane model : C.W. Nucl.Phys.B255,480(1985); Nucl.Phys.B255,480(1985);
see also B253,366(1985)see also B253,366(1985) first realistic warped modelfirst realistic warped model see Rubakov and Shaposhnikov for see Rubakov and Shaposhnikov for
earlier work ( no stable solutions, earlier work ( no stable solutions, infinitely many chiral fermions)infinitely many chiral fermions)
see Randjbar-Daemi, C.W. for see Randjbar-Daemi, C.W. for arbitrary dimensionsarbitrary dimensions
Asymptotic solution for Asymptotic solution for large tlarge t
NaturalnessNaturalness
No tuning of parameters or integration No tuning of parameters or integration constantsconstants
Radiation and matter can be implementedRadiation and matter can be implemented Asymptotic solution depends on details of Asymptotic solution depends on details of
model, e.g. solutions with constant model, e.g. solutions with constant ΩΩhh ≠ 1 ≠ 1
problem :problem :
time variation of time variation of fundamental constantsfundamental constants
primordial abundances primordial abundances for three GUT modelsfor three GUT models
T.Dent,T.Dent,S.Stern,…S.Stern,…
present present observatioobservations : 1ns : 1σσ
HeHe
DD
LiLi
three GUT modelsthree GUT models unification scale ~ Planck scaleunification scale ~ Planck scale 1) All particle physics scales ~1) All particle physics scales ~ΛΛQCDQCD
2) Fermi scale and fermion masses ~ 2) Fermi scale and fermion masses ~ unification scaleunification scale
3) Fermi scale varies more rapidly than 3) Fermi scale varies more rapidly than ΛΛQCDQCD
ΔαΔα//αα ≈ 4 10 ≈ 4 10-4 -4 allowed for GUT 1 and 3 , allowed for GUT 1 and 3 , larger for GUT 2larger for GUT 2
ΔΔln(Mln(Mnn/M/MPP) ≈40 ) ≈40 ΔαΔα//αα ≈ 0.015 allowed ≈ 0.015 allowed
Dimensional reductionDimensional reduction
Time dependent gauge Time dependent gauge couplingcoupling
stabilizing the stabilizing the couplings…couplings…
gauge couplings go to zero as volume gauge couplings go to zero as volume of internal space increasesof internal space increases
two ways to solve this problem: two ways to solve this problem: irrelevant for modes on branesirrelevant for modes on branes possible stabilization by fixed points possible stabilization by fixed points
in scale free modelsin scale free models
????????????????????????????????????????????????
Why becomes Quintessence dominant Why becomes Quintessence dominant in the present cosmological epoch ?in the present cosmological epoch ?
Are dark energy and dark matter Are dark energy and dark matter related ?related ?
Can Quintessence be explained in a Can Quintessence be explained in a fundamental unified theory ?fundamental unified theory ?
How to distinguish Q How to distinguish Q from from ΛΛ ? ?
A) Measurement A) Measurement ΩΩhh(z) H(z)(z) H(z)
i) i) ΩΩhh(z) at the time of(z) at the time of structure formation , CMB - structure formation , CMB -
emissionemission or nucleosynthesisor nucleosynthesis
ii) equation of state wii) equation of state whh((todaytoday) > -1) > -1B) Time variation of fundamental B) Time variation of fundamental
“constants”“constants”C) Apparent violation of equivalence C) Apparent violation of equivalence
principleprincipleD) Possible coupling between Dark Energy D) Possible coupling between Dark Energy
and Dark Materand Dark Mater
CosmodynamicsCosmodynamics
Cosmon mediates new long-range Cosmon mediates new long-range interactioninteraction
Range : size of the Universe – horizonRange : size of the Universe – horizon
Strength : weaker than gravityStrength : weaker than gravity
photon electrodynamicsphoton electrodynamics
graviton gravitygraviton gravity
cosmon cosmodynamicscosmon cosmodynamics
Small correction to Newton’s lawSmall correction to Newton’s law
““Fifth Force”Fifth Force”
Mediated by scalar fieldMediated by scalar field
Coupling strength: weaker than gravityCoupling strength: weaker than gravity
( nonrenormalizable interactions ~ M( nonrenormalizable interactions ~ M-2 -2 )) Composition dependence Composition dependence
violation of equivalence principleviolation of equivalence principle Quintessence: connected to time variation Quintessence: connected to time variation
of of
fundamental couplingsfundamental couplings
R.Peccei,J.Sola,C.Wetterich,Phys.Lett.B19R.Peccei,J.Sola,C.Wetterich,Phys.Lett.B195,183(1987)5,183(1987)
C.Wetterich , C.Wetterich , Nucl.Phys.B302,645(1988Nucl.Phys.B302,645(1988))
Violation of equivalence Violation of equivalence principleprinciple
Different couplings Different couplings of cosmon to of cosmon to proton and neutronproton and neutron
Differential Differential accelerationacceleration
““Violation of Violation of equivalence equivalence principle”principle”
earth
p,n
p,n
cosmon
only apparent : new “fifth force” !only apparent : new “fifth force” !
Differential accelerationDifferential acceleration
Two bodies with equal mass Two bodies with equal mass experience experience
a different acceleration !a different acceleration !
ηη = ( a = ( a11 – a – a22 ) / ( a ) / ( a11 + + aa22 ) )bound : η < 3 10-14
Cosmon coupling to Cosmon coupling to atomsatoms
Tiny !!!Tiny !!! Substantially weaker than gravity.Substantially weaker than gravity. Non-universal couplings bounded by Non-universal couplings bounded by
teststests
of equivalence principle.of equivalence principle. Universal coupling bounded by tests of Universal coupling bounded by tests of
Brans-Dicke parameter Brans-Dicke parameter ωω in solar in solar system.system.
Only very small influence on cosmology.Only very small influence on cosmology.
Cosmon coupling to Dark Cosmon coupling to Dark MatterMatter
Only bounded by cosmologyOnly bounded by cosmology Substantial coupling possibleSubstantial coupling possible Can modify scaling solution and late Can modify scaling solution and late
cosmologycosmology Role in clustering of extended Role in clustering of extended
objects ?objects ?
L. AmendolaL. Amendola
Quintessence and time Quintessence and time variation of fundamental variation of fundamental
constantsconstantsStrong, electromagnetic, weakinteractions
gravitation cosmodynamics
Generic prediction
Strength unknown
C.Wetterich , C.Wetterich , Nucl.Phys.B302,645(Nucl.Phys.B302,645(19881988))
Time varying constantsTime varying constants
It is not difficult to obtain It is not difficult to obtain quintessence potentials from higher quintessence potentials from higher dimensional or string theoriesdimensional or string theories
Exponential form rather generic Exponential form rather generic
( after Weyl scaling)( after Weyl scaling) But most models show too strong But most models show too strong
time dependence of constants !time dependence of constants !
Are fundamental Are fundamental “constants”“constants”
time dependent ?time dependent ?
Fine structure constant Fine structure constant αα (electric (electric charge)charge)
Ratio electron mass to proton massRatio electron mass to proton mass
Ratio nucleon mass to Planck massRatio nucleon mass to Planck mass
Quintessence and Quintessence and Time dependence of Time dependence of
“fundamental constants”“fundamental constants”
Fine structure constant depends on Fine structure constant depends on value ofvalue of
cosmon field : cosmon field : αα((φφ))
(similar in standard model: couplings depend (similar in standard model: couplings depend on value of Higgs scalar field)on value of Higgs scalar field)
Time evolution of Time evolution of φφ Time evolution of Time evolution of αα
Jordan,…Jordan,…
Standard – Model of Standard – Model of electroweak electroweak
interactions :interactions :Higgs - mechanismHiggs - mechanism
The masses of all fermions and gauge bosons The masses of all fermions and gauge bosons are proportional to the ( vacuum expectation ) are proportional to the ( vacuum expectation ) value of a scalar field value of a scalar field φφHH ( Higgs scalar ) ( Higgs scalar )
For electron, quarks , W- and Z- bosons :For electron, quarks , W- and Z- bosons :
mmelectron electron = h= helectron * electron * φφHH etc.etc.
Restoration of symmetryRestoration of symmetryat high temperature at high temperature in the early Universein the early Universe
High THigh TSYM SYM <<φφHH>=0>=0
Low TLow TSSBSSB<<φφHH>=>=φφ00 ≠≠ 00
high T :high T :less orderless ordermore more symmetrysymmetry
example:example:magnetsmagnets
In the hot plasma In the hot plasma of the early Universe :of the early Universe :
No difference in mass for No difference in mass for electron and muon !electron and muon !
Quintessence :Quintessence :Couplings are still varying Couplings are still varying
nownow ! !
Strong bounds on Strong bounds on the variation of couplings -the variation of couplings -interesting perspectives for interesting perspectives for
observation !observation !
baryons :
the matter of stars and humans
ΩΩbb = 0.045 = 0.045
A.Coc’05A.Coc’05
Abundancies of Abundancies of primordialprimordiallight elementslight elementsfrom from nucleosynthesisnucleosynthesis
Allowed values for variation of Allowed values for variation of fine structure constant :fine structure constant :
ΔαΔα//αα ( z=10 ( z=1010 10 ) = -1.0 10) = -1.0 10-3 -3 GUT 1GUT 1ΔαΔα//αα ( z=10 ( z=1010 10 ) = -2.7 10) = -2.7 10-4 -4 GUT 2GUT 2
C.Mueller,G.Schaefer,…C.Mueller,G.Schaefer,…
primordial abundances primordial abundances for three GUT modelsfor three GUT models
T.Dent,T.Dent,S.Stern,…S.Stern,…
present present observatioobservations : 1ns : 1σσ
HeHe
DD
LiLi
three GUT modelsthree GUT models unification scale ~ Planck scaleunification scale ~ Planck scale 1) All particle physics scales ~1) All particle physics scales ~ΛΛQCDQCD
2) Fermi scale and fermion masses ~ 2) Fermi scale and fermion masses ~ unification scaleunification scale
3) Fermi scale varies more rapidly than 3) Fermi scale varies more rapidly than ΛΛQCDQCD
ΔαΔα//αα ≈ 4 10 ≈ 4 10-4 -4 allowed for GUT 1 and 3 , allowed for GUT 1 and 3 , larger for GUT 2larger for GUT 2
ΔΔln(Mln(Mnn/M/MPP) ≈40 ) ≈40 ΔαΔα//αα ≈ 0.015 allowed ≈ 0.015 allowed
Variation of fine structure Variation of fine structure constant constant
as function of redshiftas function of redshiftThree independent data sets Three independent data sets
from Keck/HIRESfrom Keck/HIRES
ΔΔαα//αα = - 0.54 (12) = - 0.54 (12) 1010-5-5
Murphy,Webb,Flammbaum, june Murphy,Webb,Flammbaum, june 20032003
VLTVLT
ΔΔαα//αα = - 0.06 (6) = - 0.06 (6) 1010-5-5
Srianand,Chand,Petitjean,Aracil, Srianand,Chand,Petitjean,Aracil, feb.2004feb.2004
z ≈ 2
Atomic clocks and OKLOAtomic clocks and OKLO
assumes that both effects are dominated by change of fine structure constant
Time variation of coupling constants must be tiny –
would be of very high significance !
Possible signal for Quintessence
Παντα ρει
Everything is flowingEverything is flowing
Apparent violation of Apparent violation of equivalence principle equivalence principle
andand
time variation of time variation of fundamental couplingsfundamental couplings
measure both themeasure both the
cosmon – coupling to cosmon – coupling to ordinary matterordinary matter
Differential acceleration Differential acceleration ηη
For unified theories ( GUT ) :For unified theories ( GUT ) :
Q : time dependence of other parameters
ηη==ΔΔa/2aa/2a
Link between time variation of α
and violation of equivalence principle
typically : η = 10-14
if time variation of α
near Oklo upper bound
to be tested ( MICROSCOPE , …)
SummarySummary
o ΩΩhh = 0.7 = 0.7
o Q/Q/ΛΛ : dynamical und static dark energy : dynamical und static dark energy
will be distinguishablewill be distinguishable
o Q : time varying fundamental coupling Q : time varying fundamental coupling “constants” “constants”
violation of equivalence principleviolation of equivalence principle
EnEndd
Quintessence Quintessence cosmologycosmology- models -- models -
Quintessence modelsQuintessence models Kinetic function Kinetic function k(k(φφ)) : parameterizes the : parameterizes the details of the model - “kinetial”details of the model - “kinetial”
k(k(φφ) = k=const. Exponential Q.) = k=const. Exponential Q. k(k(φφ ) = exp (( ) = exp ((φφ – – φφ11)/)/αα) Inverse power law Q.) Inverse power law Q. kk²²((φφ )= “1/(2E( )= “1/(2E(φφcc – – φφ))” Crossover Q.))” Crossover Q.
possible naturalness criterion:possible naturalness criterion:
k(k(φφ=0)/ k(=0)/ k(φφtodaytoday) : not tiny or huge !) : not tiny or huge !
- else: explanation needed - - else: explanation needed -
More models …More models … Phantom energyPhantom energy ( Caldwell )( Caldwell )
negative kinetic term ( w < -1 )negative kinetic term ( w < -1 ) consistent quantum theory ?consistent quantum theory ?
K – essenceK – essence ( Amendariz-Picon, Mukhanov, Steinhardt )( Amendariz-Picon, Mukhanov, Steinhardt )
higher derivative kinetic termshigher derivative kinetic terms why derivative expansion not valid ?why derivative expansion not valid ?
Coupling cosmon / (dark ) matterCoupling cosmon / (dark ) matter ( C.W.’95, Amendola )( C.W.’95, Amendola )
why substantial coupling to dark matter and not to ordinary why substantial coupling to dark matter and not to ordinary matter ?matter ?
Non-minimal coupling to curvature scalar – f(Non-minimal coupling to curvature scalar – f(φφ) R –) R – can be brought to standard form by Weyl scaling !can be brought to standard form by Weyl scaling !
Non-local gravity Non-local gravity (C.W.’97, Reuter, Turner,..)(C.W.’97, Reuter, Turner,..)
not obvious where non-local terms come fromnot obvious where non-local terms come from
CosmonCosmon Tiny massTiny mass
mmcc ~ H ~ H
New long - range interactionNew long - range interaction
cosmon mass changes cosmon mass changes with timewith time ! !
for standard kinetic termfor standard kinetic term mmcc
22 = V” = V”
for standard exponential potential , k for standard exponential potential , k ≈ const.≈ const.
mmcc22 = V”/ k = V”/ k22 = V/( k = V/( k2 2 MM22 ) )
= 3 = 3 ΩΩh h (1 - w(1 - whh ) H ) H2 2 /( 2 k/( 2 k2 2 ) )
Quintessence becomes Quintessence becomes important “today”important “today”
Equation of stateEquation of state
p=T-V pressure p=T-V pressure kinetic energykinetic energy
ρρ=T+V energy density=T+V energy density
Equation of stateEquation of state
Depends on specific evolution of the scalar Depends on specific evolution of the scalar fieldfield
Negative pressureNegative pressure
w < 0 w < 0 ΩΩh h increases increases (with decreasing z (with decreasing z
))
w < -1/3 expansion of the Universe isw < -1/3 expansion of the Universe is
acceleratingaccelerating
w = -1 cosmological constantw = -1 cosmological constant
late universe withlate universe withsmall radiation small radiation component :component :
Transition to Transition to cosmon dominated universecosmon dominated universe
Large value k >> 1 : universe is Large value k >> 1 : universe is dominated by scalar fielddominated by scalar field
k increases rapidly : evolution of k increases rapidly : evolution of scalar fied essentially stopsscalar fied essentially stops
Realistic and natural quintessence: Realistic and natural quintessence:
k changes from small to large values k changes from small to large values after structure formationafter structure formation
crossover quintessencecrossover quintessence
k(φ) increase strongly for φ corresponding to present epoch
Example (LKT) :
exponential quintessence:
Hebecker,…Hebecker,…
Cosmon dark matter ?Cosmon dark matter ?
Can cosmon Can cosmon fluctuations account fluctuations account for dark matter ?for dark matter ?
Cosmon can vary in Cosmon can vary in spacespace