cosmodynamics. quintessence and solution of cosmological constant problem should be related !
TRANSCRIPT
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CosmodynamicsCosmodynamics
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Quintessence and Quintessence and solution of solution of
cosmological constant cosmological constant problem should be problem should be
related !related !
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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
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Dirac’s hypothesisDirac’s hypothesis
The very small dimensionless The very small dimensionless numbers in physics are due to huge numbers in physics are due to huge age of the universe .age of the universe .
(A)may be true forratio of dark energyover M4
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Dilatation symmetryDilatation symmetry Lagrange density:Lagrange density:
Dilatation symmetry forDilatation symmetry for
Conformal symmetry for Conformal symmetry for δδ=0=0
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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 : decreases for
increasing increasing χχ !! !! E>0 : crossover quintessenceE>0 : crossover quintessence
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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 !
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WeylWeyl scalingscaling
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)
No additional constant !No additional constant !
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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 k where k grows large k²²((φφ )= )=δδ((χχ)/4 )/4
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
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““Fundamental” Fundamental” InteractionsInteractions
Strong, electromagnetic, weakinteractions
gravitation cosmodynamics
On astronomical length scales:
graviton
+
cosmon
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CosmonCosmon Tiny massTiny mass
mmcc ~ H ~ H
New long - range interactionNew long - range interaction
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cosmon masscosmon mass
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 ) )
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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
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““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))
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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,…
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Field dependent gauge Field dependent gauge couplingcoupling
( gauge invariance ( gauge invariance maintained )maintained )
for GUT : C.Hill ; Q.Shafi , CW
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GUT : running of GUT : running of electromagneticelectromagnetic
and strong gauge coupling and strong gauge coupling relatedrelated
strong effect from variation of nucleon mass for time dependent couplings ! X.Calmet , H.Fritzsch
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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
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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
z ≈ 2
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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 leads to small Crossover Quintessence leads to small variation of couplings at low z as compared variation of couplings at low z as compared to z ≈ 2 !to z ≈ 2 !
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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 !
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Variation of fine structure Variation of fine structure constant constant
as function of redshiftas function of redshift
Webb et al
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Cosmon and time variation Cosmon and time variation of couplingsof couplings
small coupling of cosmon to matter small coupling of cosmon to matter due to fixed points behaviordue to fixed points behavior
close to fixed point :small time evolution of couplingscoupling to matter weaker than gravitational strength
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dependence of fixed point dependence of fixed point on on δδ
could induce observable could induce observable effecteffect
adjusting b6 to reproduce results by Webb et al:
smaller for Srianand et al !
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Time variation of coupling constants is tiny –
would be of very high significance !
Possible signal for Quintessence
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Παντα ρει
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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
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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
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Differential acceleration Differential acceleration ηη
For unified theories ( GUT ) :For unified theories ( GUT ) :
Q : time dependence of other parameters
ηη==ΔΔa/2aa/2a
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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
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This leads to differential This leads to differential acceleration !acceleration !
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Atomic clocks and OKLOAtomic clocks and OKLO
assumes that both effects are dominated by change of fine structure constant
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small change of couplings small change of couplings in spacein space
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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
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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 ?
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Cosmon dark matterCosmon dark matter
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