Dunkle Energie –Ein kosmisches Raetsel

Quintessence

Dark energy –Dark energy –a cosmic mystery a cosmic mystery

C.WetterichC.Wetterich

A.Hebecker,M.Doran,M.Lilley,J.Schwindt,A.Hebecker,M.Doran,M.Lilley,J.Schwindt,C.MC.Müüller,G.Schller,G.Schääfer,E.Thommes,fer,E.Thommes,R.CaldwellR.Caldwell

What is our What is our UniverseUniversemade of ?made of ?

fire , air, water, soil !

Quintessence !

critical densitycritical density ρρcc =3 H² M² =3 H² M² critical energy density of the critical energy density of the

universe universe ( M : reduced Planck-mass , H : Hubble ( M : reduced Planck-mass , H : Hubble

parameter )parameter )

ΩΩbb==ρρbb//ρρcc

fraction in baryons fraction in baryons energy density in baryons over energy density in baryons over

critical energy densitycritical energy density

Composition of the Composition of the universeuniverse

ΩΩb b = 0.045= 0.045

ΩΩdmdm= 0.225= 0.225

ΩΩh h = 0.73= 0.73

gravitational lens , HST

ΩΩmm≈0.3≈0.3

spatially flat universespatially flat universe

theory (inflationary universe )theory (inflationary universe )

ΩΩtottot =1.0000……….x =1.0000……….x

observation ( Boomerang,WMAP )observation ( Boomerang,WMAP )

ΩΩtottot =1.02 (0.02) =1.02 (0.02)

ΩΩtottot = = 11

picture of the big bangpicture of the big bang

mean values

Ωtot =1.02

Ωm =0.27

Ωb =0.045

Ωdm =0.225

Dark EnergyDark Energy

ΩΩmm + X = 1 + X = 1

ΩΩmm : 30% : 30%

ΩΩhh : 70% : 70% Dark Dark

EnergyEnergyh : homogenous , often ΩΛ instead of Ωh

Dark Energy :

homogeneously distributed

What is Dark Energy ?

Cosmological Constant or Quintessence ?

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

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 observableOnly 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 scalar generated 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

CosmonCosmon Scalar field changes its value even Scalar field changes its value even

in the in the presentpresent cosmological epoch cosmological 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 massTiny 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

Evolution of cosmon fieldEvolution of cosmon field

Field equationsField equations

Potential V(Potential V(φφ) determines details of ) determines details of the modelthe model

e.g. e.g. V(V(φφ) =M) =M4 4 exp( - exp( - φφ/M )/M )

for increasing for increasing φφ the potential the potential decreases towards zero !decreases towards zero !

Cosmic Attractors Cosmic 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

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 :

small early and large small early and large presentpresent

dark energydark energy fraction in dark energy has fraction in dark energy has

substantially increased since end of substantially increased since end of structure formationstructure formation

expansion of universe accelerates in expansion of universe accelerates in present epochpresent epoch

How can quintessence be How can quintessence be distinguished from a distinguished from a

cosmological constant ?cosmological constant ?

Time dependence of dark Time dependence of dark energyenergy

cosmological constant : Ωh ~ t² ~ (1+z)-3

M.Doran,…

Measure this curve !Measure this curve !

Early dark energyEarly dark energy

A few percent in the early A few percent in the early UniverseUniverse

Not possible for a cosmological Not possible for a cosmological constantconstant

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))

Are fundamental Are fundamental “constants”“constants”

time dependent ?time dependent ?

Fine structure constant Fine structure constant αα (electric (electric charge)charge)

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,…

Field dependent gauge Field dependent gauge couplingcoupling

( gauge invariance ( gauge invariance maintained )maintained )

for GUT : C.Hill ; Q.Shafi , CW

GUT : running of GUT : running of electromagneticelectromagnetic

and strong gauge coupling and strong gauge coupling relatedrelated

strong effect from variation of nucleon mass for time dependent couplings ! X.Calmet , H.Fritzsch

Where to look for time Where to look for time variation of fundamental variation of fundamental

couplings ?couplings ? NucleosynthesisNucleosynthesis Molecular absorption lines in the Molecular absorption lines in the

light of distant Quasarslight of distant Quasars Oklo natural reactorOklo natural reactor Atomic clocksAtomic clocks CMBCMB

A.CocA.Coc

Abundancies of Abundancies of primordialprimordiallight elementslight elementsfrom from nucleosynthesisnucleosynthesis

ifif present 2-sigma deviation of He –abundance present 2-sigma deviation of He –abundancefrom CMB/nucleosynthesis prediction would be from CMB/nucleosynthesis prediction would be confirmed :confirmed :

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,…

Variation of fine structure Variation of fine structure constant constant

as function of redshiftas function of redshift

Webb et al Srianand et alSrianand et al

Variation of fine structure Variation of fine structure constantconstant

Three independent data sets from Three independent data sets from Keck/HIRESKeck/HIRES

ΔΔαα//αα = - 0.54 (12) 10 = - 0.54 (12) 10-5-5

Murphy,Webb,Flammbaum, june 2003Murphy,Webb,Flammbaum, june 2003

VLTVLT

ΔΔαα//αα = - 0.06 (6) 10 = - 0.06 (6) 10-5-5

Srianand,Chand,Petitjean,Aracil, feb.2004Srianand,Chand,Petitjean,Aracil, feb.2004

z ≈ 2

Crossover quintessence andCrossover quintessence andtime variation of time variation of

fundamental “constants”fundamental “constants”

Upper bounds for relative variation of the Upper bounds for relative variation of the

fine structure constantfine structure constant Oklo natural reactor Oklo natural reactor ΔΔαα//αα < 10 < 10 -7 -7

z=0.13z=0.13 Meteorites ( Re-decay ) Meteorites ( Re-decay ) ΔΔαα//αα < 3 10 < 3 10 -7 -7

z=0.45z=0.45

Crossover Quintessence compatible with QSOCrossover Quintessence compatible with QSO

and upper bounds !and upper bounds !

Time evolution of fundamental Time evolution of fundamental couplings traces time evolution couplings traces time evolution of quintessenceof quintessence

todaytoday wwhh close to -1 : close to -1 :

• Small kinetic energySmall kinetic energy• Slow change of Slow change of φφ• Slow change of Slow change of αα

Very small Very small ΔαΔα//αα for low z !for low z !

Variation of fine structure Variation of fine structure constant constant

as function of redshiftas function of redshift

Webb et al

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 flowseverything flows

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

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 principleprinciple

earth

p,n

p,n

cosmon

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 by 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

????????????????????????????????????????????????

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 ?

Quintessence and Quintessence and solution of solution of

cosmological constant cosmological constant problem should be problem should be

related !related !

QuintessenceQuintessenceandand

fundamental mass scalefundamental mass scale

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 observableOnly ratios of mass scales are observable

Example :Example :

Field Field χχ denotes scale of transition denotes 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…)

Dilatation symmetryDilatation symmetry Lagrange density:Lagrange density:

Dilatation symmetry forDilatation symmetry for

Conformal symmetry for Conformal symmetry for δδ=0=0

Dilatation anomalyDilatation anomaly

V~V~χχ4-A 4-A , M, Mpp((χχ )~ )~ χχ

V/MV/Mpp4 4 ~ ~ χχ-A -A : :

decreases for increasing decreases for increasing χχ !! !!

E>0 : crossover quintessenceE>0 : crossover quintessence

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 !

WeylWeyl scalingscaling

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 !

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

EnEndd

A few referencesA few references

C.Wetterich , Nucl.Phys.B302,668(1988) , received 24.9.1987C.Wetterich , Nucl.Phys.B302,668(1988) , received 24.9.1987

P.J.E.Peebles,B.Ratra , Astrophys.J.Lett.325,L17(1988) , received 20.10.1987P.J.E.Peebles,B.Ratra , Astrophys.J.Lett.325,L17(1988) , received 20.10.1987

B.Ratra,P.J.E.Peebles , Phys.Rev.D37,3406(1988) , received 16.2.1988B.Ratra,P.J.E.Peebles , Phys.Rev.D37,3406(1988) , received 16.2.1988

J.Frieman,C.T.Hill,A.Stebbins,I.Waga , Phys.Rev.Lett.75,2077(1995)J.Frieman,C.T.Hill,A.Stebbins,I.Waga , Phys.Rev.Lett.75,2077(1995)

P.Ferreira, M.Joyce , Phys.Rev.Lett.79,4740(1997)P.Ferreira, M.Joyce , Phys.Rev.Lett.79,4740(1997)

C.Wetterich , Astron.Astrophys.301,321(1995)C.Wetterich , Astron.Astrophys.301,321(1995)

P.Viana, A.Liddle , Phys.Rev.D57,674(1998)P.Viana, A.Liddle , Phys.Rev.D57,674(1998)

E.Copeland,A.Liddle,D.Wands , Phys.Rev.D57,4686(1998)E.Copeland,A.Liddle,D.Wands , Phys.Rev.D57,4686(1998)

R.Caldwell,R.Dave,P.Steinhardt , Phys.Rev.Lett.80,1582(1998)R.Caldwell,R.Dave,P.Steinhardt , Phys.Rev.Lett.80,1582(1998)

P.Steinhardt,L.Wang,I.Zlatev , Phys.Rev.Lett.82,896(1999)P.Steinhardt,L.Wang,I.Zlatev , Phys.Rev.Lett.82,896(1999)

ΩΩtottot=1=1

Dark Energy :

prediction:

The expansion of the Universe accelerates today !

Perlmutter 2003

Supernova cosmologySupernova cosmology

Riess et al. 2004Riess et al. 2004

Structure formation : Structure formation : fluctuation spectrumfluctuation spectrum

Waerbeke

CMB agrees with

galaxy distribution

Lyman – α forest

and

gravitational lensingeffect !

consistent cosmological model !

Composition of the Composition of the UniverseUniverse

ΩΩb b = 0.045 = 0.045 visible visible clumpingclumping

ΩΩdmdm= 0.225 = 0.225 invisibleinvisible clumpingclumping

ΩΩh h = 0.73 = 0.73 invisibleinvisible homogeneoushomogeneous

Dilatation anomalyDilatation anomaly

Quantum fluctuations responsible Quantum fluctuations responsible forfor

dilatation anomalydilatation anomaly Running couplings: Running couplings: hypothesishypothesis

Renormalization scale Renormalization scale μμ : : ( momentum scale )( momentum scale )

λλ~(~(χχ//μμ) ) -A-A

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 ! ) Relative increase of dark energy in present Relative increase of dark energy in present cosmological epochcosmological epoch

Dilatation anomalyDilatation anomaly Computation of running couplings ( beta Computation of running couplings ( beta

functions ) needs unified theory !functions ) needs unified theory ! Dominant contribution from modes with Dominant contribution from modes with

momenta ~momenta ~χχ ! ! No prejudice on “natural value “ of No prejudice on “natural value “ of

anomalous dimension should be inferred anomalous dimension should be inferred from tiny contributions at QCD- momentum from tiny contributions at QCD- momentum scale !scale !

Almost flat direction in potential for Almost flat direction in potential for φφ : : Pseudo-Goldstone boson of dilatation Pseudo-Goldstone boson of dilatation

symmetrysymmetry

Dynamics of Dynamics of quintessencequintessence

CosmonCosmon : 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

QuintessenceQuintessence modelsmodels 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 -

Simple parameterization of Simple parameterization of quintessencequintessence

parameter b natural “time” variable

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 formationDark energy slows down structure formation

ΩΩh h < 10% during structure formation< 10% during structure formation

Substantial Substantial increaseincrease of of ΩΩhh(t)(t) since structure has since structure has formed! formed!

negative wnegative whh

Question “why now” is back ( in mild form )Question “why now” is back ( in mild form )

P.Ferreira,M.JoyceP.Ferreira,M.Joyce

Fluctuation spectrumFluctuation spectrum

Caldwell,Doran,Müller,Schäfer,…

Anisotropy of cosmic Anisotropy of cosmic background radiationbackground radiation

Caldwell,Doran,Müller,Schäfer,…

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) > -1

B) Time variation of fundamental B) Time variation of fundamental “constants”“constants”

““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 dependenceComposition 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))

Relative change of HeRelative change of He44 – – abundance vs. relative abundance vs. relative change of couplingschange of couplings

C.Mueller, G.Schaefer, …C.Mueller, G.Schaefer, …