Dunkle Energie – Ein kosmisches Raetsel Quintessence

Quintessence 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

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

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

What is Dark Energy ? Cosmological Constant or Quintessence ?

Dynamics of Dark Energy

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 ?

( ρ + λ) λ ≠ 0

asymptotic solution for cosmological constant (k=0)

problems with small λ no symmetry explanation for λ/M 4 = no symmetry explanation for λ/M 4 = quantum fluctuations contribute quantum fluctuations contribute

Banks Weinberg Linde Anthropic principle

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 equations Field equations 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 matter ^ ^

Cosmological equations

M → ^M asymptotic solution for large time

exponential potential constant fraction in dark energy

General mechanism for cosmic attractor

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

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)

many models …

“kinetial” choose field variable such that potential has standard units advantage: φ acts as dark energy clock in cosmology A.Hebecker,… M=1

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. possible naturalness criterion: possible naturalness criterion: k(φ=0) : not tiny or huge ! k(φ=0) : not tiny or huge ! - else: explanation needed - - else: explanation needed -

crossover quintessence k(φ) increase strongly for φ corresponding to present epoch example: exponential quintessence:

Quintessence becomes important “today”

scale factor as “time”-variable

determine kinetial k(φ) by observation !

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cosmological equations