Dunkle Energie – Ein kosmisches Raetsel Dark Energy- a cosmic mystery

Dark Energy – a cosmic mystery C.Wetterich A.Hebecker,M.Doran,M.Lilley,J.Schwindt, C.Müller,G.Schäfer,E.Thommes, R.Caldwell

What is our Universe made of ?

fire, air, water, soil ! Quintessence !

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

Composition of the universe Ω b = Ω b = Ω dm = Ω dm = Ω h = 0.73 Ω h = 0.73

~60,000 of >300,000 galaxies baryons dust dust Ω b =0.045 Ω b =0.045 only 5 percent of our universe only 5 percent of our universe consist of known consist of known matter ! matter ! SDSS

Abell 2255 Cluster ~300 Mpc

Ω b =0.045 from nucleosynthesis, cosmic background radiation

Dark Matter Ω m = 0.27 total “matter” Ω m = 0.27 total “matter” Most matter is dark ! Most matter is dark ! So far tested only through gravity So far tested only through gravity Every local mass concentration gravitational potential Every local mass concentration gravitational potential Orbits and velocities of stars and galaxies measurement of gravitational potential Orbits and velocities of stars and galaxies measurement of gravitational potential and therefore of local matter distribution and therefore of local matter distribution

Gravitationslinsen gravitational lens, HST

spatially flat universe theory (inflationary universe ) theory (inflationary universe ) Ω tot =1.0000……….x Ω tot =1.0000……….x observation ( WMAP ) observation ( WMAP ) Ω tot =1.02 (0.02) Ω tot =1.02 (0.02) Ω tot = 1

picture of the big bang

NASA/GSFC Chuck Bennett (PI) Michael Greason Bob Hill Gary Hinshaw Al Kogut Michele Limon Nils Odegard Janet Weiland Ed Wollack Princeton Chris Barnes Norm Jarosik Eiichiro Komatsu Michael Nolta UBC Mark Halpern Chicago Stephan Meyer Brown Greg Tucker UCLA Ned Wright Science Team: Wilkinson Microwave Anisotropy Probe A partnership between NASA/GSFC and Princeton Lyman Page Hiranya Peiris David Spergel Licia Verde

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 + X = 1 Ω m + X = 1 Ω m : 30% Ω m : 30% Ω h : 70% Dark Energy Ω h : 70% Dark Energy h : homogenous, often Ω Λ instead of Ω h

Dark Energy : homogeneously distributed

Dark Energy : prediction: The expansion of the Universe accelerates today !

Perlmutter 2003

Supernova cosmology Riess et al. 2004

Dark energy and SN Ω M = 0.29 Ω M = (SN alone, for Ω tot =1) (SN alone, for Ω tot =1)

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

Structure formation : fluctuation spectrum Waerbeke CMB agrees with galaxy distribution Lyman – α forest and gravitational lensing effect !

consistent cosmological model !

Composition of the Universe Ω b = visible clumping Ω b = visible clumping Ω dm = invisible clumping Ω dm = invisible clumping Ω h = 0.73 invisible homogeneous Ω h = 0.73 invisible homogeneous

Dunkle Energie – Ein kosmisches Raetsel Dark Energy- a cosmic mystery

What is Dark Energy ? Cosmological Constant or Quintessence ?

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

Cosm. Const. | Quintessence static | dynamical

Cosmological mass scales Energy density Energy density ρ ~ ( 2.4×10 -3 eV ) - 4 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 = ˉ¹²¹ homogeneous dark energy: ρ h /M 4 = ˉ¹²¹ matter: ρ m /M= ˉ¹²¹ matter: ρ m /M 4 = ˉ¹²¹

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

Quintessence Dynamical dark energy, generated by scalar field generated by scalar field (cosmon) (cosmon) C.Wetterich,Nucl.Phys.B302(1988)668, P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17,

Cosmon Scalar field changes its value even in the present cosmological epoch 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 Potential und kinetic energy of cosmon contribute to the energy density of the Universe Time - variable dark energy : Time - variable dark energy : ρ h (t) decreases with time ! ρ h (t) decreases with time !

Cosmon Tiny mass Tiny mass m c ~ H m c ~ H New long - range interaction New long - range interaction

“Fundamental” Interactions Strong, electromagnetic, weak interactions gravitationcosmodynamics On astronomical length scales: graviton + cosmon

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

Cosmological equations

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

Dynamics of quintessence Cosmon  : scalar singlet field Cosmon  : scalar singlet field Lagrange density L = V + ½ k(φ)  Lagrange density L = V + ½ k(φ)  (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:  =276 today:  =276

Quintessence models Kinetic function k(φ) : parameterizes the Kinetic function k(φ) : parameterizes the details of the model - “kinetial” details of the model - “kinetial” k(φ) = k=const. Exponential Q. k(φ) = k=const. Exponential Q. k(φ ) = exp ((φ – φ 1 )/α) Inverse power law Q. k(φ ) = exp ((φ – φ 1 )/α) Inverse power law Q. k²(φ )= “1/(2E(φ c – φ))” Crossover Q. k²(φ )= “1/(2E(φ c – φ))” Crossover Q. Naturalness criterion: Naturalness criterion: k(φ=0)/ k(φ today ) : not tiny or huge ! k(φ=0)/ k(φ today ) : not tiny or huge ! - else: explanation needed - - else: explanation needed -

Quintessence becomes important “today”

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

Negative pressure w < 0 Ω h increases w < 0 Ω h increases w < -1/3 expansion of the Universe is w < -1/3 expansion of the Universe is accelerating accelerating w = -1 cosmological constant w = -1 cosmological constant

Quintessence becomes important “today”

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,…

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

Early quintessence slows down the growth of structure

Fluctuation spectrum Caldwell,Doran,Müller,Schäfer,…

Anisotropy of cosmic background radiation Caldwell,Doran,Müller,Schäfer,…

How to distinguish Q from Λ ? A) Measurement Ω h (z) H(z) i) Ω h (z) at the time of i) Ω h (z) at the time of structure formation, CMB - emission structure formation, CMB - emission or nucleosynthesis or nucleosynthesis ii) equation of state w h ( today ) > -1 ii) equation of state w h ( today ) > -1 B) Time variation of fundamental “constants”

Are fundamental “constants” time dependent ? Fine structure constant α (electric charge) Ratio nucleon mass to Planck mass

“Fifth Force” Mediated by scalar field Mediated by scalar field Coupling strength: weaker than gravity Coupling strength: weaker than gravity ( nonrenormalizable interactions ~ M -2 ) ( nonrenormalizable interactions ~ M -2 ) Composition dependence Composition dependence violation of equivalence principle violation of equivalence principle Quintessence: connected to time variation of Quintessence: connected to time variation of fundamental couplings fundamental couplings R.Peccei,J.Sola,C.Wetterich,Phys.Lett.B195,183(1987) C.Wetterich, Nucl.Phys.B302,645(1988)

Quintessence and Time dependence of “fundamental constants” Fine structure constant depends on value of Fine structure constant depends on value of cosmon field : α(φ) cosmon field : α(φ) (similar in standard model: couplings depend on value of Higgs scalar field) (similar in standard model: couplings depend on value of Higgs scalar field) Time evolution of φ Time evolution of φ Time evolution of α Time evolution of α Jordan,…

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

Crossover quintessence and time variation of fundamental “constants” Upper bounds for relative variation of the Upper bounds for relative variation of the fine structure constant fine structure constant Oklo natural reactor Δ α/α < z=0.13 Oklo natural reactor Δ α/α < z=0.13 Meteorites ( Re-decay ) Δ α/α < z=0.45 Meteorites ( Re-decay ) Δ α/α < z=0.45 Crossover Quintessence compatible with QSO Crossover Quintessence compatible with QSO and upper bounds ! and upper bounds !

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

Time evolution of fundamental couplings traces time evolution of quintessence today w h close to -1 : today w h close to -1 : Small kinetic energy Small kinetic energy Slow change of φ Slow change of φ Slow change of α Slow change of α Very small Δα/α for low z ! Very small Δα/α for low z !

Time variation of coupling constants is tiny – would be of very high significance ! Possible signal for Quintessence

Παντα ρει

Cosmodynamics Cosmon mediates new long-range interaction Range : size of the Universe – horizon Range : size of the Universe – horizon Strength : weaker than gravity Strength : weaker than gravity photon electrodynamics photon electrodynamics graviton gravity graviton gravity cosmon cosmodynamics 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 p,n cosmon

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 = if Webb et al. is right…. to be tested by MICROSCOPE

Summary o Ω h = 0.7 o Q/Λ : dynamical und static dark energy will be distinguishable will be distinguishable o Q : time varying fundamental coupling “constants” violation of equivalence principle 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 !

End

A few references C.Wetterich, Nucl.Phys.B302,668(1988), received P.J.E.Peebles,B.Ratra, Astrophys.J.Lett.325,L17(1988), received B.Ratra,P.J.E.Peebles, Phys.Rev.D37,3406(1988), received 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)

NOT LENSED (randomly aligned) LENSED N Galaxies Averaged shape Shear estimate Waerbeke

cosmological weak gravitational lensing 1deg Waerbeke

Cosmic Shear (68%) Ranges for  m,  h from WMAPext, SNIa and Cosmic Shear Waerbeke ΩhΩhΩhΩh

Growth of density fluctuations Matter dominated universe with constant Ω h : Matter dominated universe with constant Ω h : Dark energy slows down structure formation Dark energy slows down structure formation Ω h < 10% during structure formation Ω h < 10% during structure formation Substantial increase of Ω h (t) since structure has formed! Substantial increase of Ω h (t) since structure has formed! negative w h negative w h Question “why now” is back ( in mild form ) Question “why now” is back ( in mild form ) P.Ferreira,M.Joyce

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

Cosmon and fundamental mass scales Assume all mass parameters are proportional to scalar field χ (GUTs, superstrings,…) Assume all mass parameters are proportional to scalar field χ (GUTs, superstrings,…) M p ~ χ, m proton ~ χ, Λ QCD ~ χ, M W ~ χ,… M p ~ χ, m proton ~ χ, Λ QCD ~ χ, M W ~ χ,… χ may evolve with time χ may evolve with time m n /M : ( almost ) constant - observation ! m n /M : ( almost ) constant - observation ! Only ratios of mass scales are observable

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

Dilatation anomaly Quantum fluctuations responsible for Quantum fluctuations responsible for dilatation anomaly dilatation anomaly Running couplings: Running couplings: V~χ 4-A, M p (χ )~ χ V~χ 4-A, M p (χ )~ χ V/M p 4 ~ χ -A : decreases for increasing χ V/M p 4 ~ χ -A : decreases for increasing χ E>0 : crossover quintessence E>0 : crossover quintessence

Cosmology Cosmology : χ increases with time ! ( due to coupling of χ to curvature scalar ) “ late time cosmology explores the ultraviolet” “ late time cosmology explores the ultraviolet” for large χ the ratio V/M 4 decreases to zero Effective cosmological constant vanishes asymptotically for large t !

Weyl scaling Cosmology : χ increases with time ! (“ late time cosmology explores the ultraviolet”) (“ late time cosmology explores the ultraviolet”) Weyl scaling : g μν → (M/χ) 2 g μν, φ/M = ln (χ 4 /V(χ)) φ/M = ln (χ 4 /V(χ)) Exponential potential : V = M 4 exp(-φ/M)

Crossover Quintessence ( like QCD gauge coupling) ( like QCD gauge coupling) critical χ where δ grows large critical φ where k grows large k²(φ )= “1/(2E(φ c – φ)/M)” k²(φ )= “1/(2E(φ c – φ)/M)” if  c  ≈ 276/M ( tuning ! ) if  c  ≈ 276/M ( tuning ! ) Relative increase of dark energy in present Relative increase of dark energy in present cosmological epoch cosmological epoch

W 94 GHz Dipole Removed

WMAP Angular Power Spectrum Anisotropy of CMB Angle amplitude of fluctuations

Tonry et al Supernova cosmology Ω h =0.7

209 SN Ia and medians Tonry et al Ω h =0.7 Ω m =0.3