Dunkle Energie – Ein kosmisches Raetsel Quintessence.
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Transcript of Dunkle Energie – Ein kosmisches Raetsel Quintessence.
Quintessence Quintessence
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
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
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
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
Dark EnergyDark Energy
ΩΩmm + X = 1 + X = 1
ΩΩmm : 30% : 30%
ΩΩhh : 70% : 70% Dark Dark
EnergyEnergyh : homogenous , often ΩΛ instead of Ωh
Structure formation : Structure formation : fluctuation spectrumfluctuation spectrum
Waerbeke
CMB agrees with
galaxy distribution
Lyman – α forest
and
gravitational lensingeffect !
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
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 ?
asymptotic solution for asymptotic solution for cosmological constant cosmological constant
(k=0)(k=0)
problems with small problems with small λλ
no symmetry explanation for no symmetry explanation for λλ/M/M4 4
=10=10 -120 -120
quantum fluctuations contributequantum fluctuations contribute
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 ?
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 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 !
exponential potentialexponential potentialconstant fraction in dark constant fraction in dark
energyenergy
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
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)
““kinetial”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 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.
possible naturalness criterion:possible naturalness criterion:
k(k(φφ=0) : not tiny or huge !=0) : not tiny or huge !
- else: explanation needed - - else: explanation needed -
crossover quintessencecrossover quintessence
k(φ) increase strongly for φ corresponding to present epoch
example:
exponential quintessence: