with exponential coupling Extended Quintessence - DESY Library · DESY Theory Workshop 2004, DESY,...
Transcript of with exponential coupling Extended Quintessence - DESY Library · DESY Theory Workshop 2004, DESY,...
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Extended QuintessenceExtended Quintessencewith exponential couplingwith exponential coupling
C. C. BaccigalupiBaccigalupi (SISSA, Trieste), G. Mangano ((SISSA, Trieste), G. Mangano (UnivUniv. of . of NaplesNaples))
DESY Theory Workshop 2004DESY Theory Workshop 200428th Sept 28th Sept –– 1st October1st October
DESY HamburgDESY Hamburg
Valeria Pettorino (Valeria Pettorino (UnivUniv. of . of NaplesNaples))
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
CMB
SupernovaeIa
Modern cosmologyModern cosmology
Large Scale Structures
HST
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
Content of the UniverseContent of the Universe
Part of the energy in the universe which does not cluster.
73.0=ΩDE
225.0=ΩDM
045.0=Ωb
1=Ω tot
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ρρρρmρρρρrρρρρΛΛΛΛ
a
Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
Dark Dark EEnergynergy scalar fieldscalar field
Dark energy
Cosmological constant
ρρρρmρρρρrρρρρΛΛΛΛ
a
Cosmological constant
φ
V (φ)
basic model
Constant energy contribution
Why so small?Why same order right now?
Dynamical energy contribution
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
DE and DE and tracker fieldstracker fields
Tracker fields
Dark Energy
Cosmological constant
A subclass of Quintessence models admits a useful property:any solution within a wide range of initial conditions converges toan attractor solution, providing the amount of energy density required today.
Liddle & Scherrer, Steinhardt et al
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
wwQQ and and tracker fieldstracker fieldsIn most tracker models wQ
today is predicted to be too different from – 1 to be allowed by observations. The potential V needs to be flattened, thus shrinking the range of initial conditions.
wQ < — 0.78 at 95%
CMBCMBLSSLSS HH Sup Sup IaIa
As the allowed range shrinks, tracker fields become less appealing.
Weller & Lewis 2003
13.015.091.0 +
−−=Qw
Spergel et al 2003
Tegmark 2004
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
Coupling Dark energyCoupling Dark energy
Essential to understand how Dark Energy interacts with other entities
Dark Matter
Dark Energy
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Perrotta BaccigalupiMatarrese 2000
Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
Dark energyDark energy
Non coupled DE
Dark energy
Cosmological constant
Dark Energy& Dark Matter
Dark energy & Gravity
Coupled DE
Tracker fields
Amendola 2000
V.P. Mangano, Miele 2002
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
Scalar tensor theoriesScalar tensor theories
= 1
Ricci scalarScalar field
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
The The couplingcoupling
Induced Gravity (IG)
Exponential Coupling
Non minimal Coupling (NMC)
RRF 2)( ξφφ = RGRRF 2
16)( ξφ
πφ += ( )ξφ
πφ exp
16)(
GRRF =
Scalar tensor theories of gravity
Dilatonic-inspired coupling
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
Cosmological expansionCosmological expansion
In a FRW space, the relevant equations change
…both for the background…
…and for the field
Where we have used
RFaφ2
2
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
Observational constraintsObservational constraints
yr/10 11−<Time variation of the gravitational constant
Local laboratories and solar system experiments
Nucleosynthesis
This bound guaranties a value for 4He and Deuterium in concordance with recent extimates.
6.04.1 ≤∆≤− N 3.01.0 ≤≤− ξφ
256.0228.0 ≤≤ pY55 102.3/104.2 −− ×≤≤× HD
Effects on the J.B.D. parameter(Bertotti et al. Nature 2004)
Effects induced on photon trajectories from G variation
JBDωπξ 16=
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
RR--boostboost
The coupling generates a new purely gravitational effect called R-boost
02
2 22...
=+−+ φφφφ VaRFa
H
When 013
0 ≠≅aF
R mρ there is an effective gravitational potential acting on the field
Baccigalupi Matarrese Perrotta 2000
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M
Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
Energy density behaviourEnergy density behaviour
The RDE is dominated by the R-boost
The minimally coupled solution is equivalent to a cosmological constant in RDE. It moves only recently, when it reaches the tracker solution
V becomes important: end of slow-roll; ρφ reaches the required value today
radiation
matter
Anlytical R-boost
Exp
Minimally coupled Q
NMC
exp 0=•
begφ ωJBD = 105
= 1610-2
22
2. RFaH φφ ≈ slow roll
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M
Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
RDE & MDERDE & MDE
const+= τξπ
τφ log16
3)(begr
m φτπρ
ρξτφ +=0
0 83
4)(
τ∝a 2τ∝aRDE MDE
Analytical solutions of the K.G. equation
Independent of φbeg
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
RR--boost effectsboost effects
R-boost (exp)
R-boost NMCφ (exp)
φ NMC
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
φφφφφφφφee is an is an attractorattractor
StabilityStabilityIf we look for scaling solutions of the K.G. equation:
when the background is:
we find that the R-boost solution is given by:
and F must be:
B(m,n) = 0 for exp coupling
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Valeria Pettorino Valeria Pettorino –– Napoli, Napoli, ItalyItaly DESY DESY TheoryTheory Workshop 2004Workshop 2004, DESY, , DESY, Hamburg Hamburg 28th 28th SeptSept –– 1st 1st OctoberOctober2004
ConclusionsConclusions•The coupling generates a purely gravitational effect called R-boost.
•The R-boost dynamics is the most relevant effect during the initial motion of the field, dominated by kinetic energy.
•The exponential coupling gives a stronger effect than the power law NMC model both on ρφ and on φ.
•The R-boost is an attractor, independently of V, thatrestores a large basin of attraction even if the true potential is flat.
•The exponential coupling, of dilatonic-inspiration, is the simplest expression for the coupling to give scaling solutions to K.G. equation.
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Extended QuintessenceExtended Quintessencewith exponential couplingwith exponential coupling
DESY Theory Workshop 2004DESY Theory Workshop 200428th Sept 28th Sept –– 1st October1st October
DESY HamburgDESY Hamburg