Dunkle Energie –Ein kosmisches Raetsel

Dark Energy-a cosmic mystery

Dark Energy –Dark Energy –a cosmic mysterya 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

~60,000 of >300,000 galaxies

baryonsbaryons

dustdust ΩΩbb=0.045=0.045 only 5 only 5

percent of percent of our our universeuniverse

consist of consist of known known

matter !matter !

SDSS

Abell 2255 Cluster~300 Mpc

Ωb=0.045

from nucleosynthesis,cosmic background radiation

Dark MatterDark Matter ΩΩmm = 0.27 total “matter” = 0.27 total “matter” Most matter is dark !Most matter is dark ! So far tested only through gravitySo far tested only through gravity Every local mass concentration Every local mass concentration

gravitational potentialgravitational potential Orbits and velocities of stars and galaxies Orbits and velocities of stars and galaxies

measurement of gravitational potential measurement of gravitational potential

and therefore of local matter distributionand therefore of local matter distribution

GravitationslinsenGravitationslinsen

gravitational lens , HST

spatially flat universespatially flat universe

theory (inflationary universe )theory (inflationary universe )

ΩΩtottot =1.0000……….x =1.0000……….x

observation ( WMAP )observation ( WMAP )

ΩΩtottot =1.02 (0.02) =1.02 (0.02)

ΩΩtottot = = 11

picture of the big bangpicture of the big bang

NASA/GSFCChuck Bennett (PI)Michael GreasonBob Hill Gary Hinshaw Al KogutMichele LimonNils OdegardJanet WeilandEd Wollack

PrincetonChris Barnes Norm Jarosik Eiichiro KomatsuMichael Nolta

UBCMark Halpern

ChicagoStephan Meyer

BrownGreg Tucker

UCLANed Wright

Science Team:

Wilkinson Microwave Anisotropy ProbeA partnership between NASA/GSFC and Princeton

Lyman PageHiranya PeirisDavid SpergelLicia Verde

mean values

Ωtot =1.02

Ωm =0.27

Ωb =0.045

Ωdm =0.225

ΩΩtottot=1=1

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

Dark Energy :

prediction:

The expansion of the Universe accelerates today !

Perlmutter 2003

Supernova cosmologySupernova cosmology

Riess et al. 2004Riess et al. 2004

Dark Dark energy energy and SNand SN

ΩΩM M = 0.29= 0.29 +0.05-+0.05-

0.030.03

(SN alone, for (SN alone, for ΩΩtottot=1)=1)

Structure formationStructure formation

Structures in the Universe grow from tinyStructures in the Universe grow from tiny fluctuations in density distributionfluctuations in density distribution

stars , galaxies, clustersstars , galaxies, clusters

OneOne primordial fluctuation spectrum primordial fluctuation spectrum describesdescribes

allall correlation functions ! correlation functions !

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

Dunkle Energie –Ein kosmisches Raetsel

Dark Energy-a cosmic mystery

What is Dark Energy ?

Cosmological Constant or Quintessence ?

Cosmological ConstantCosmological Constant

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

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 equationField equation

Potential V(Potential V(φφ) determines details of the ) determines details of the modelmodel

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

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

Cosmological equationsCosmological equations

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

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.

Naturalness criterion:Naturalness criterion:

k(k(φφ=0)/ k(=0)/ k(φφtodaytoday) : not tiny or huge !) : not tiny or huge !

- else: explanation needed - - else: explanation needed -

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 increasesincreases

w < -1/3 expansion of the w < -1/3 expansion of the Universe isUniverse is

acceleratingaccelerating

w = -1 cosmological constantw = -1 cosmological constant

Quintessence becomes Quintessence becomes important “today”important “today”

SN and equation of stateSN and equation of state

Riess et al. 2004Riess et al. 2004

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,…

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

Early quintessence slows down Early quintessence slows down the the

growth of structuregrowth of structure

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”

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

““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))

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,…

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

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 !

Variation of fine structure Variation of fine structure constant constant

as function of redshiftas function of redshift

Webb et al

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 !

Time variation of coupling constants is tiny –

would be of very high significance !

Possible signal for Quintessence

Παντα ρει

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 Webb et al. is right….

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 !

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)

NOT LENSED (randomly aligned)

LENSED

N Galaxies

Averaged shape

Shear estimate

0e

γe

Waerbeke

cosmological weakcosmological weak

gravitational lensinggravitational lensing

1deg1degWaerbeke

Cosmic Shear (68%)

Ranges for m, h from WMAPext, SNIa and Cosmic Shear

Waerbeke

ΩΩhh

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

Cosmological ConstantCosmological Constant

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 ?

Cosmon and Cosmon and fundamental mass scalesfundamental mass scales

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 mmnn/M : ( almost ) constant - /M : ( almost ) constant - observationobservation !!

Only ratios of mass scales are Only ratios of mass scales are observableobservable

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:

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 to curvature scalar )scalar )

“ “ late time cosmology explores the late time cosmology explores the ultraviolet”ultraviolet”

for large for large χχ the ratio V/M the ratio V/M4 4 decreases to decreases to zerozero

Effective cosmological constant Effective cosmological constant vanishes asymptotically for large t !vanishes asymptotically for large t !

WeylWeyl scalingscaling

Cosmology : Cosmology : χχ increases with time ! increases with time !

(“ late time cosmology explores the (“ late time cosmology explores the ultraviolet”)ultraviolet”)

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)

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 where k grows large

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

W 94 GHzDipole Removed

WMAP Angular Power Spectrum

Anisotropy of CMBAnisotropy of CMBAngle

amplitude offluctuations

Tonry et al. 2003

Supernova Supernova cosmologycosmology

ΩΩhh=0.7=0.7

209 SN Ia and medians209 SN Ia and mediansTonry et al. 2003

ΩΩhh=0.=0.77ΩΩmm==0.30.3