dunkle energie – ein kosmisches raetsel dark energy- a cosmic mystery
Post on 15-Jan-2016
219 views
TRANSCRIPT
Dunkle Energie –Ein kosmisches Raetsel
Dark Energy-a cosmic mystery
Dark Energy –Dark Energy –a cosmic mysterya cosmic mystery
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
What is our What is our UniverseUniversemade of ?made of ?
fire , air, water, soil !
Quintessence !
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
~60,000 of >300,000 galaxies
baryonsbaryons
dustdust ΩΩbb=0.045=0.045 only 5 only 5
percent of percent of our our universeuniverse
consist of consist of known known
matter !matter !
SDSS
Abell 2255 Cluster~300 Mpc
Ωb=0.045
from nucleosynthesis,cosmic background radiation
Dark MatterDark Matter ΩΩmm = 0.27 total “matter” = 0.27 total “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 galaxies Orbits and velocities of stars and galaxies
measurement of gravitational potential measurement of gravitational potential
and therefore of local matter distributionand therefore of local matter distribution
GravitationslinsenGravitationslinsen
gravitational lens , HST
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
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
mean values
Ωtot =1.02
Ωm =0.27
Ωb =0.045
Ωdm =0.225
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
Dark Energy :
homogeneously distributed
Dark Energy :
prediction:
The expansion of the Universe accelerates today !
Perlmutter 2003
Supernova cosmologySupernova cosmology
Riess et al. 2004Riess et al. 2004
Dark Dark energy energy and SNand SN
ΩΩM M = 0.29= 0.29 +0.05-+0.05-
0.030.03
(SN alone, for (SN alone, for ΩΩtottot=1)=1)
Structure formationStructure formation
Structures in the Universe grow from tinyStructures in the Universe grow from tiny fluctuations in density distributionfluctuations in density distribution
stars , galaxies, clustersstars , galaxies, clusters
OneOne primordial fluctuation spectrum primordial fluctuation spectrum describesdescribes
allall correlation functions ! correlation functions !
Structure formation : Structure formation : fluctuation spectrumfluctuation spectrum
Waerbeke
CMB agrees with
galaxy distribution
Lyman – α forest
and
gravitational lensingeffect !
consistent cosmological model !
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
Dunkle Energie –Ein kosmisches Raetsel
Dark Energy-a cosmic mystery
What is Dark Energy ?
Cosmological Constant or Quintessence ?
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 ?
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 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 equationField equation
Potential V(Potential V(φφ) determines details of the ) determines details of the modelmodel
e.g. e.g. V(V(φφ) =M) =M4 4 exp( - exp( - φφ/M )/M )
for increasing for increasing φφ the potential decreases the potential decreases towards zerotowards zero
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
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.
Naturalness criterion:Naturalness criterion:
k(k(φφ=0)/ k(=0)/ k(φφtodaytoday) : not tiny or huge !) : not tiny or huge !
- else: explanation needed - - else: explanation needed -
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 increasesincreases
w < -1/3 expansion of the w < -1/3 expansion of the Universe isUniverse is
acceleratingaccelerating
w = -1 cosmological constantw = -1 cosmological constant
Quintessence becomes Quintessence becomes important “today”important “today”
SN and equation of stateSN and equation of state
Riess et al. 2004Riess et al. 2004
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,…
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
Fluctuation spectrumFluctuation spectrum
Caldwell,Doran,Müller,Schäfer,…
Anisotropy of cosmic Anisotropy of cosmic background radiationbackground radiation
Caldwell,Doran,Müller,Schäfer,…
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 - structure formation , CMB -
emissionemission 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”
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
““Fifth Force”Fifth Force”
Mediated by scalar fieldMediated by scalar field
Coupling strength: weaker than gravityCoupling strength: weaker than gravity
( nonrenormalizable interactions ~ M( nonrenormalizable interactions ~ M-2 -2 )) Composition dependenceComposition dependence
violation of equivalence principleviolation of equivalence principle Quintessence: connected to time variation Quintessence: connected to time variation
of of
fundamental couplingsfundamental couplings
R.Peccei,J.Sola,C.Wetterich,Phys.Lett.B19R.Peccei,J.Sola,C.Wetterich,Phys.Lett.B195,183(1987)5,183(1987)
C.Wetterich , C.Wetterich , Nucl.Phys.B302,645(1988Nucl.Phys.B302,645(1988))
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,…
Variation of fine structure Variation of fine structure constant constant
as function of redshiftas function of redshift
Webb et al Srianand et alSrianand et al
Variation of fine structure Variation of fine structure constantconstant
Three independent data sets from Three independent data sets from Keck/HIRESKeck/HIRES
ΔΔαα//αα = - 0.54 (12) 10 = - 0.54 (12) 10-5-5
Murphy,Webb,Flammbaum, june 2003Murphy,Webb,Flammbaum, june 2003
VLTVLT
ΔΔαα//αα = - 0.06 (6) 10 = - 0.06 (6) 10-5-5
Srianand,Chand,Petitjean,Aracil, feb.2004Srianand,Chand,Petitjean,Aracil, feb.2004
Crossover quintessence andCrossover quintessence andtime variation of time variation of
fundamental “constants”fundamental “constants”
Upper bounds for relative variation of the Upper bounds for relative variation of the
fine structure constantfine structure constant Oklo natural reactor Oklo natural reactor ΔΔαα//αα < 10 < 10 -7 -7
z=0.13z=0.13 Meteorites ( Re-decay ) Meteorites ( Re-decay ) ΔΔαα//αα < 3 10 < 3 10 -7 -7
z=0.45z=0.45
Crossover Quintessence compatible with QSOCrossover Quintessence compatible with QSO
and upper bounds !and upper bounds !
Variation of fine structure Variation of fine structure constant constant
as function of redshiftas function of redshift
Webb et al
Time evolution of fundamental Time evolution of fundamental couplings traces time evolution couplings traces time evolution of quintessenceof quintessence
todaytoday wwhh close to -1 : close to -1 :
• Small kinetic energySmall kinetic energy• Slow change of Slow change of φφ• Slow change of Slow change of αα
Very small Very small ΔαΔα//αα for low z !for low z !
Time variation of coupling constants is tiny –
would be of very high significance !
Possible signal for Quintessence
Παντα ρει
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 principleprinciple
earth
p,n
p,n
cosmon
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 Webb et al. is right….
to be tested by MICROSCOPE
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
????????????????????????????????????????????????
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 ?
Quintessence and Quintessence and solution of solution of
cosmological constant cosmological constant problem should be problem should be
related !related !
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)
NOT LENSED (randomly aligned)
LENSED
N Galaxies
Averaged shape
Shear estimate
0e
γe
Waerbeke
cosmological weakcosmological weak
gravitational lensinggravitational lensing
1deg1degWaerbeke
Cosmic Shear (68%)
Ranges for m, h from WMAPext, SNIa and Cosmic Shear
Waerbeke
ΩΩhh
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
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 ?
Cosmon and Cosmon and fundamental mass scalesfundamental mass scales
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 mmnn/M : ( almost ) constant - /M : ( almost ) constant - observationobservation !!
Only ratios of mass scales are Only ratios of mass scales are observableobservable
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 to curvature scalar )scalar )
“ “ late time cosmology explores the late time cosmology explores the ultraviolet”ultraviolet”
for large for large χχ the ratio V/M the ratio V/M4 4 decreases to decreases to zerozero
Effective cosmological constant Effective cosmological constant vanishes asymptotically for large t !vanishes asymptotically for large t !
WeylWeyl scalingscaling
Cosmology : Cosmology : χχ increases with time ! increases with time !
(“ late time cosmology explores the (“ late time cosmology explores the ultraviolet”)ultraviolet”)
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)
Crossover QuintessenceCrossover Quintessence
( like QCD gauge ( like QCD gauge coupling)coupling)
critical critical χχ where where δδ grows large grows largecritical critical φφ where k grows large where k grows large
kk²²((φφ )= “1/(2E( )= “1/(2E(φφcc – – φφ)/M)”)/M)”
ifif cc≈ 276/M ( tuning ! )≈ 276/M ( tuning ! ) Relative increase of dark energy in present Relative increase of dark energy in present cosmological epochcosmological epoch
W 94 GHzDipole Removed
WMAP Angular Power Spectrum
Anisotropy of CMBAnisotropy of CMBAngle
amplitude offluctuations
Tonry et al. 2003
Supernova Supernova cosmologycosmology
ΩΩhh=0.7=0.7
209 SN Ia and medians209 SN Ia and mediansTonry et al. 2003
ΩΩhh=0.=0.77ΩΩmm==0.30.3