Dunkle Energie –Ein kosmisches Raetsel

Dark Energy-a cosmic mystery

QuintessenceQuintessence

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.Caldwell,M.BartelmannR.Caldwell,M.Bartelmann

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

30 % + 70 %30 % + 70 %

What is Dark Energy ?What is Dark Energy ?

Abell 2255 Cluster~300 Mpc

Matter : Everything that clumpsMatter : Everything that clumps

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

Dark MatterDark 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 Orbits and velocities of stars and

galaxies measurement of gravitational galaxies measurement of gravitational potential potential

and therefore of local matter and therefore of local matter distributiondistribution

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 ( WMAP )observation ( WMAP )

ΩΩtottot =1.02 (0.02) =1.02 (0.02)

ΩΩtottot = = 11

picture of the big bangpicture of the big bang

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

Space between clumpsSpace between clumps is not empty : is not empty :

Dark Energy !Dark Energy !

Dark Energy density isDark Energy density isthe same at every point of the same at every point of

space space

“ homogeneous “ “ homogeneous “

No force –No force –“ In what direction should it “ In what direction should it

draw ? “draw ? “

Two important Two important predictionspredictions

The expansion of the Universe

accelerates today !

Structure Structure formation : formation : OneOne primordial primordial

fluctuation- fluctuation- spectrumspectrum

consistent cosmological model !

Composition of the Composition of the UniverseUniverse

ΩΩb b = 0.045 = 0.045 visible visible clumpingclumping

ΩΩdmdm= 0.22 = 0.22 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- 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 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 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

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 )Homogeneous 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 !

““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 !

Cosmological equationsCosmological equations

cosmon +matterexample:example:

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

in the in the presentpresent 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 massTiny mass

mmcc ~ H ~ H

New long - range interactionNew long - range interaction

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

cosmon mass changes cosmon mass changes with time !with 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 ) )

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

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

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

No reason why w shouldNo reason why w shouldbe constant in time !be constant in time !

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 Measure ΩΩhh(z) !(z) !

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

A few percent Early Dark A few percent Early Dark EnergyEnergy

If linear power spectrum fixed today If linear power spectrum fixed today ( ( σσ8 8 ) :) :

More Structure at More Structure at high z !high z !

Bartelmann,Doran,…Bartelmann,Doran,…

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 - emissionstructure formation , CMB - emission 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”

C) Apparent violation of equivalence C) Apparent violation of equivalence principleprinciple

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 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 myon !electron and myon !

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 !

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,…

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

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

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

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 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

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 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 !

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 !

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

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

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 ?

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)

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

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 -

SN and equation of stateSN and equation of state

Riess et al. 2004Riess et al. 2004

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 principle”principle”

earth

p,n

p,n

cosmon

only apparent : new “fifth force” !only apparent : new “fifth force” !

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

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