dunkle energie – ein kosmisches raetsel
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Dunkle Energie –Ein kosmisches Raetsel
Quintessence-a dynamical Dark Energy
QuintessenceQuintessence
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.Caldwell,M.Bartelmann,K.KarwanR.Caldwell,M.Bartelmann,K.Karwan
What is our universe What is our universe made of ?made of ?
quintessence !fire , air,
water, soil !
Dark Energy Dark Energy dominates the Universedominates the Universe
Energy - density in the Energy - density in the UniverseUniverse
==
Matter + Dark EnergyMatter + Dark Energy
30 % + 70 %30 % + 70 %
What is Dark Energy ?What is Dark Energy ?
Abell 2255 Cluster~300 Mpc
Matter : Everything that clumpsMatter : Everything that clumps
gravitational lens , HST
ΩΩmm= 0.3= 0.3
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
Space between clumpsSpace between clumps is not empty : is not empty :
Dark Energy !Dark Energy !
Dark Energy density isDark Energy density isthe same at every point of the same at every point of
space space
“ homogeneous “ “ homogeneous “
No force –No force –“ In what direction should it “ In what direction should it
draw ? “draw ? “
Two important Two important predictionspredictions
The expansion of the Universe
accelerates today !
Structure Structure formation : formation : OneOne primordial primordial
fluctuation- fluctuation- spectrumspectrum
Baryon - PeakBaryon - Peak
SDSSSDSS
galaxy – galaxy – correlation –correlation –functionfunction
consistent cosmological model !
Composition of the Composition of the UniverseUniverse
ΩΩb b = 0.045 = 0.045 visible visible clumpingclumping
ΩΩdmdm= 0.22 = 0.22 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- Einstein -- Einstein -
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 observable !Only 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
Prediction :Prediction :
homogeneous dark energy homogeneous dark energyinfluences recent cosmologyinfluences recent cosmology
- of same order as dark - of same order as dark matter -matter -
Original models do not fit the present observationsOriginal models do not fit the present observations……. modifications. modifications
QuintessenceQuintessence
Cosmon – Field Cosmon – Field φφ(x,y,z,t)(x,y,z,t)
similar to electric field , but no direction similar to electric field , but no direction ( scalar field )( scalar field )Homogeneous und isotropic Universe : Homogeneous und isotropic Universe :
φφ(x,y,z,t)=(x,y,z,t)=φφ(t)(t)
Potential und kinetic energy of the cosmon Potential und kinetic energy of the cosmon -field-field
contribute to a dynamical energy density of contribute to a dynamical energy density of the Universe ! the Universe !
““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 !
CosmonCosmon Scalar field changes its value even Scalar field changes its value even
in the in the presentpresent cosmological epochcosmological 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
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
cosmon mass changes cosmon mass changes with time !with time !
for standard kinetic termfor standard kinetic term mmcc
22 = V” = V”
for standard exponential potential , k for standard exponential potential , k = const.= const.
mmcc22 = V”/ k = V”/ k22 = V/( k = V/( k2 2 MM22 ) )
= 3 = 3 ΩΩh h (1 - w(1 - whh ) H ) H2 2 /( 2 k/( 2 k2 2 ) )
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)/ k(=0)/ k(φφtodaytoday) : not tiny or huge !) : not tiny or huge !
- else: explanation needed - - else: explanation needed -
More models …More models … Phantom energyPhantom energy ( Caldwell )( Caldwell )
negative kinetic term ( w < -1 )negative kinetic term ( w < -1 ) consistent quantum theory ?consistent quantum theory ?
K – essenceK – essence ( Amendariz-Picon, Mukhanov, Steinhardt )( Amendariz-Picon, Mukhanov, Steinhardt )
higher derivative kinetic termshigher derivative kinetic terms why derivative expansion not valid ?why derivative expansion not valid ?
Coupling cosmon / (dark ) matterCoupling cosmon / (dark ) matter ( C.W., Amendola )( C.W., Amendola )
why substantial coupling to dark matter and not to ordinary why substantial coupling to dark matter and not to ordinary matter ?matter ?
Non-minimal coupling to curvature scalar – f(Non-minimal coupling to curvature scalar – f(φφ) R -) R - can be brought to standard form by Weyl scaling !can be brought to standard form by Weyl scaling !
kinetialkinetial
Small almost constant k :Small almost constant k : Small almost constant Small almost constant ΩΩhh
Large k :Large k : Cosmon dominated universe ( like Cosmon dominated universe ( like
inflation )inflation )
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
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 increases increases (with decreasing z (with decreasing z
))
w < -1/3 expansion of the Universe isw < -1/3 expansion of the Universe is
acceleratingaccelerating
w = -1 cosmological constantw = -1 cosmological constant
late universe withlate universe withsmall radiation small radiation component :component :
small early and large small early and large presentpresent
dark energydark energy fraction in dark energy has fraction in dark energy has
substantially increased since end of substantially increased since end of structure formationstructure formation
expansion of universe accelerates in expansion of universe accelerates in present epochpresent epoch
Quintessence becomes Quintessence becomes important “today”important “today”
No reason why w shouldNo reason why w shouldbe constant in time !be constant in time !
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,…
Measure Measure ΩΩhh(z) !(z) !
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
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
A few percent Early Dark A few percent Early Dark EnergyEnergy
If linear power spectrum fixed today If linear power spectrum fixed today ( ( σσ8 8 ) :) :
More Structure at More Structure at high z !high z !
Bartelmann,Doran,…Bartelmann,Doran,…
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 - emissionstructure formation , CMB - emission 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”
C) Apparent violation of equivalence C) Apparent violation of equivalence principleprinciple
Quintessence and time Quintessence and time variation of fundamental variation of fundamental
constantsconstantsStrong, electromagnetic, weakinteractions
gravitation cosmodynamics
Generic prediction
Strength unknown
C.Wetterich , C.Wetterich , Nucl.Phys.B302,645(Nucl.Phys.B302,645(19881988))
Time varying constantsTime varying constants
It is not difficult to obtain It is not difficult to obtain quintessence potentials from higher quintessence potentials from higher dimensional or string theoriesdimensional or string theories
Exponential form rather generic Exponential form rather generic
( after Weyl scaling)( after Weyl scaling) But most models show too strong But most models show too strong
time dependence of constants !time dependence of 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
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,…
Standard – Model of Standard – Model of electroweak electroweak
interactions :interactions :Higgs - mechanismHiggs - mechanism
The masses of all fermions and gauge bosons The masses of all fermions and gauge bosons are proportional to the ( vacuum expectation ) are proportional to the ( vacuum expectation ) value of a scalar field value of a scalar field φφHH ( Higgs scalar ) ( Higgs scalar )
For electron, quarks , W- and Z- bosons :For electron, quarks , W- and Z- bosons :
mmelectron electron = h= helectron * electron * φφHH etc.etc.
Restoration of symmetryRestoration of symmetryat high temperature at high temperature in the early Universein the early Universe
High THigh TSYM SYM <<φφHH>=0>=0
Low TLow TSSBSSB<<φφHH>=>=φφ00 ≠≠ 00
high T :high T :less orderless ordermore more symmetrysymmetry
example:example:magnetsmagnets
In the hot plasma In the hot plasma of the early Universe :of the early Universe :
No difference in mass for No difference in mass for electron and myon !electron and myon !
Quintessence :Quintessence :Couplings are still varying Couplings are still varying
nownow ! !
Strong bounds on Strong bounds on the variation of couplings -the variation of couplings -interesting perspectives for interesting perspectives for
observation !observation !
A.CocA.Coc
Abundancies of Abundancies of primordialprimordiallight elementslight elementsfrom from nucleosynthesisnucleosynthesis
ifif present 2-sigma deviation of He –abundance present 2-sigma deviation of He –abundancefrom CMB/nucleosynthesis prediction would be from CMB/nucleosynthesis prediction would be confirmed :confirmed :
ΔαΔα//αα ( z=10 ( z=1010 10 ) = -1.0 10) = -1.0 10-3 -3 GUT 1GUT 1ΔαΔα//αα ( z=10 ( z=1010 10 ) = -2.7 10) = -2.7 10-4 -4 GUT 2GUT 2
C.Mueller,G.Schaefer,…C.Mueller,G.Schaefer,…
Time variation of coupling constants must be tiny –
would be of very high significance !
Possible signal for Quintessence
Παντα ρει
Everything is flowingEverything is flowing
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
Quintessence and Quintessence and solution of solution of
cosmological constant cosmological constant problem should be problem should be
related !related !
????????????????????????????????????????????????
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 ?
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)
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 principle”principle”
earth
p,n
p,n
cosmon
only apparent : new “fifth force” !only apparent : new “fifth force” !
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 time variation of α near Oklo upper
bound
to be tested by MICROSCOPE
Variation of fine structure Variation of fine structure constant constant
as function of redshiftas function of redshiftThree independent data sets Three independent data sets
from Keck/HIRESfrom Keck/HIRES
ΔΔαα//αα = - 0.54 (12) = - 0.54 (12) 1010-5-5
Murphy,Webb,Flammbaum, june Murphy,Webb,Flammbaum, june 20032003
VLTVLT
ΔΔαα//αα = - 0.06 (6) = - 0.06 (6) 1010-5-5
Srianand,Chand,Petitjean,Aracil, Srianand,Chand,Petitjean,Aracil, feb.2004feb.2004
z ≈ 2
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