Quintessence

Dunkle Energie – Ein kosmisches Raetsel

Dark energy – a cosmic mystery

C.Wetterich

A.Hebecker,M.Doran,M.Lilley,J.Schwindt, C.M

üller,G.Schäfer,E.Thommes, R.Caldwell

What is our Universe made of ?

Quintessence !

fire , air, water, soil !

critical density

 ρ c =3 H² M² critical energy density of the universe ( M : reduced Planck-mass , H : Hubble parameter )  Ω b =ρ b /ρ c fraction in baryons energy density in baryons over critical energy density

Composition of the universe

Ω b = 0.045

Ω dm = 0.225

Ω h = 0.73

Ω

b

=0.045

from nucleosynthesis, cosmic background radiation

Dark Matter

 Ω m = 0.27 total “matter”  Most matter is dark !

 So far tested only through gravity  Every local mass concentration gravitational potential  Orbits and velocities of stars and galaxies measurement of gravitational potential and therefore of local matter distribution

Ω m ≈0.3

gravitational lens , HST

spatially flat universe

Ω tot = 1  theory (inflationary universe )  Ω tot =1.0000……….x

observation ( Boomerang,WMAP ) Ω tot =1.02 (0.02)

picture of the big bang

mean values Ω tot =1.02

Ω m =0.27

Ω b =0.045

Ω dm =0.225

Ω

tot

=1

Dark Energy

Ω m Ω m Ω h

+ X = 1 : 30% : 70% Dark Energy

h : homogenous , often Ω Λ instead of Ω h

Dark Energy : homogeneously distributed

Confirmation by Supernovae

Perlmutter 2003

Supernova cosmology

Riess et al. 2004

Structure formation

Structures in the Universe grow from tiny fluctuations in density distribution stars , galaxies, clusters One all primordial fluctuation spectrum describes correlation functions !

Waerbeke

Structure formation : fluctuation spectrum

CMB agrees with galaxy distribution Lyman – α forest and gravitational lensing effect !

What is Dark Energy ?

Cosmological Constant or Quintessence ?

Cosmological Constant - Einstein -

 Constant λ compatible with all symmetries  No time variation in contribution to energy density  Why so small ? λ/M 4 = 10 -120  Why important just today ?

Cosm. Const. | Quintessence static | dynamical

Cosmological mass scales  Energy density ρ ~ ( 2.4

× 10 -3 eV )

- 4

  Reduced Planck mass M=2.44

× 10 18 GeV Newton’s constant G N =(8πM²) Only ratios of mass scales are observable !

homogeneous dark energy: ρ h /M 4 = 6.5 10ˉ¹²¹ matter: ρ m /M 4 = 3.5 10ˉ¹²¹

Time evolution

 ρ m /M 4 ~ aˉ ³ ~ tˉ ² tˉ 3/2 matter dominated universe radiation dominated universe  ρ r /M 4 ~ aˉ 4 ~ t -2 radiation dominated universe Huge age small ratio Same explanation for small dark energy?

Quintessence

Dynamical dark energy , generated by scalar field (cosmon)

C.Wetterich,Nucl.Phys.B302(1988)668, 24.9.87

P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, 20.10.87

Prediction : homogeneous dark energy influences recent cosmology - of same order as dark matter -

Original models do not fit the present observations …. modifications

Cosmon



Scalar field changes its value even in the present cosmological epoch



Potential und kinetic energy of cosmon contribute to the energy density of the Universe



Time - variable dark energy : ρ h (t) decreases with time !

Cosmon



Tiny mass



m c ~ H



New long - range interaction

“Fundamental” Interactions

Strong, electromagnetic, weak interactions On astronomical length scales: graviton + cosmon gravitation cosmodynamics

Evolution of cosmon field

Field equations Potential V(φ) determines details of the model e.g. V(φ) =M 4 exp( - φ/M ) for increasing φ the potential decreases towards zero !

Cosmic Attractors Solutions independent of initial conditions

typically V~t -2 φ ~ ln ( t ) Ω h ~ const.

details depend on V(φ) or kinetic term early cosmology

Quintessence becomes important “today”

Equation of state

p=T-V pressure kinetic energy ρ=T+V energy density Equation of state Depends on specific evolution of the scalar field

Negative pressure

 w < 0 Ω h increases (with decreasing z ) late universe with small radiation component :  w < -1/3 expansion of the Universe is accelerating  w = -1 cosmological constant

small early and large present dark energy

fraction in dark energy has substantially increased since end of structure formation expansion of universe accelerates in present epoch

SN and equation of state

Riess et al. 2004

How can quintessence be distinguished from a cosmological constant ?

Time dependence of dark energy

cosmological constant : Ω

h ~ t² ~ (1+z) -3

M.Doran,…

Measure this curve !

Early dark energy

A few percent in the early Universe Not possible for a cosmological constant

Quintessence and time variation of fundamental constants

Strong, electromagnetic, weak interactions Generic prediction Strength unknown C.Wetterich , Nucl.Phys.B302,645(1988 ) gravitation cosmodynamics

Are fundamental “constants” time dependent ?

Fine structure constant α (electric charge) Ratio nucleon mass to Planck mass

Quintessence and time dependence of “fundamental constants”



Fine structure constant depends on value of cosmon field : α(φ) (similar in standard model: couplings depend on value of Higgs scalar field)



Time evolution of φ Time evolution of α

Jordan,…

Field dependent gauge coupling ( gauge invariance maintained )

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

GUT : running of electromagnetic and strong gauge coupling related strong effect from variation of nucleon mass for time dependent couplings !

X.Calmet , H.Fritzsch

Where to look for time variation of fundamental couplings ?

 Nucleosynthesis  Molecular absorption lines in the light of distant Quasars  Oklo natural reactor  Atomic clocks  CMB

Abundancies of primordial light elements from nucleosynthesis A.Coc

if present 2-sigma deviation of He –abundance from CMB/nucleosynthesis prediction would be confirmed : Δα/α ( z=10 10 ) = -1.0 10 -3 GUT 1 Δα/α ( z=10 10 ) = -2.7 10 -4 GUT 2 C.Mueller,G.Schaefer,…

Variation of fine structure constant as function of redshift Webb et al Srianand et al

Variation of fine structure constant

Three independent data sets from Keck/HIRES Δ α/α = - 0.54 (12) 10 -5 Murphy,Webb,Flammbaum, june 2003 VLT Δ α/α = - 0.06 (6) 10 -5 Srianand,Chand,Petitjean,Aracil, feb.2004

z ≈ 2

Crossover quintessence and time variation of fundamental “constants”

  Upper bounds for relative variation of the fine structure constant Oklo natural reactor Δ α/α < 10 -7 z=0.13

Meteorites ( Re-decay ) Δ α/α < 3 10 -7 z=0.45

 Crossover Quintessence compatible with QSO and upper bounds !

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

today w h close to -1 :

Small kinetic energy Slow change of φ Slow change of α

Very small Δα/α for low z !

Variation of fine structure constant as function of redshift Webb et al

Atomic 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 flows

Cosmodynamics

Cosmon mediates new long-range interaction Range : size of the Universe – horizon Strength : weaker than gravity photon electrodynamics graviton gravity cosmon cosmodynamics Small correction to Newton’s law

Violation of equivalence principle

Different couplings of cosmon to proton and neutron Differential acceleration Violation of equivalence principle earth cosmon p,n p,n

Differential acceleration η

For unified theories ( GUT ) : Q : time dependence of other parameters η=Δa/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

Summary

o Ω h = 0.7

o Q/Λ : dynamical und static dark energy will be distinguishable o Q : time varying fundamental coupling “constants” violation of equivalence principle

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

Why becomes Quintessence dominant in the present cosmological epoch ?

Are dark energy and dark matter related ?

Can Quintessence be explained in a fundamental unified theory ?

Quintessence and solution of cosmological constant problem should be related !

Quintessence and fundamental mass scale

Fundamental mass scale

 Unification fixes parameters with dimensions  Special relativity : c  Quantum theory : h  Unification with gravity : fundamental mass scale ( Planck mass , string tension , …)

Fundamental mass scale

 Fixed parameter or dynamical scale ?

 Dynamical scale Field  Dynamical scale compared to what ?

momentum versus mass ( or other parameter with dimension )

Cosmon and fundamental mass scale

 Assume all mass parameters are proportional to scalar field χ (GUTs, superstrings,…)  M p ~ χ , m proton ~ χ , Λ QCD ~ χ , M W ~ χ ,…   χ may evolve with time : cosmon m n /M : ( almost ) constant -

observation

!

Only ratios of mass scales are observable

Example : Field χ denotes scale of transition from higher dimensional physics to effective four dimensional description in theory without fundamental mass parameter (except for running of dimensionless couplings…)

Dilatation symmetry

 Lagrange density:  Dilatation symmetry for  Conformal symmetry for δ=0

Dilatation anomaly

 V~χ 4-A , M p (χ )~ χ 

V/M p 4 ~ χ -A : decreases for increasing χ !!

 E>0 : crossover quintessence

Cosmology

Cosmology : χ increases with time !

( due to coupling of χ to curvature scalar ) for large χ the ratio V/M 4 decreases to zero Effective cosmological constant vanishes asymptotically for large t !

Weyl scaling

Weyl scaling : g μν → (M/χ) 2 g μν , φ/M = ln (χ 4 /V(χ))

Exponential potential : V = M 4 No additional constant !

exp(-φ/M)

Realistic cosmology

Hypothesis on running couplings yields realistic cosmology for suitable values of A , E , φ c

End

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

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

B.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) P.Ferreira, M.Joyce , Phys.Rev.Lett.79,4740(1997) C.Wetterich , Astron.Astrophys.301,321(1995) P.Viana, A.Liddle , Phys.Rev.D57,674(1998) E.Copeland,A.Liddle,D.Wands , Phys.Rev.D57,4686(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)

Dilatation anomaly

 Quantum fluctuations responsible for  dilatation anomaly Running couplings: hypothesis   Renormalization scale μ : ( momentum scale ) λ~(χ/μ) -A

Crossover Quintessence

( like QCD gauge coupling) critical χ where δ grows large critical φ where k grows large k

²

( φ )=δ(χ)/4 k

²

( φ )= “1/(2E(φ

c

– φ)/M)” if j c ≈ 276/M ( tuning ! ) Relative increase of dark energy in present cosmological epoch

Dilatation anomaly

    Computation of running couplings ( beta functions ) needs unified theory !

Dominant contribution from modes with momenta ~χ !

No prejudice on “natural value “ of anomalous dimension should be inferred from tiny contributions at QCD- momentum scale !

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

Dynamics of quintessence

 Cosmon j : scalar singlet field  Lagrange density L = V + ½

k(φ)

j j (units: reduced Planck mass M=1)  Potential : V=exp[ j]  “Natural initial value” in Planck era j=0  today: j

=276

Quintessence models

 Kinetic function k(φ) : parameterizes the details of the model - “kinetial”    k(φ) = k=const. Exponential Q.

k(φ ) = exp ((φ – φ

1

)/α) Inverse power law Q.

k²(φ )= “1/(2E(φ

c

– φ))” Crossover Q.

 possible naturalness criterion: k(φ=0)/ k(φ today ) : not tiny or huge !

- else: explanation needed -

Early quintessence slows down the growth of structure

Growth of density fluctuations

 Matter dominated universe with constant Ω h : P.Ferreira,M.Joyce

  Dark energy slows down structure formation Ω h < 10% during structure formation Substantial increase of Ω h (t) since structure has formed! negative w h  Question “why now” is back ( in mild form )

Fluctuation spectrum

Caldwell,Doran,Müller,Schäfer,…

Anisotropy of cosmic background radiation

Caldwell,Doran,Müller,Schäfer,…