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