Probing the Reheating with Probing the Reheating with Astrophysical Observations Astrophysical Observations
Jérôme Jérôme MartinMartin
Institut d’Astrophysique de Paris (IAP)Institut d’Astrophysique de Paris (IAP)
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[In collaboration with K. Jedamzik & M. Lemoine, arXiv:1002.3039, arXiv:1002.3278 and C. Ringeval, arXiv:1004.5525]
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Outline
Introduction
A brief and naive description of reheating
Constraining the reheating with the CMB observations
Preheating: can it affect the behaviour of cosmological perturbations?
Production of gravitational waves during preheating
Conclusions
321/04/23
Inflation is a phase of accelerated expansion taking place in the very early Universe. The scale factor is such that
This assumption allows us to solve several problems of the standard hot Big Bang model:
•Horizon problem
•Flatness problem
•Monopoles problem …
Usually +3p>0 (eg p=0) and the expansion is decelerated. Inflation requires negative pressure
Hot Big Bang problems
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Field theory is the correct description at high energies.
A natural realization is a scalar field slowly rolling down its flat potential
Inflation ends by violation of the slow-roll conditions or by instability
After inflation, the field oscillates at the bottom of its potential: this is the reheating
Inflation in brief
Inflation in a nutshell
Large field
Small field
Hybrid inflation
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End of Inflation (I)
Slow-roll phase
Oscillatory phase
p=2
p=4
p=2 p=4
Violation of Slow-roll
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End of Inflation (II)
Oscillatory phase
p=2 p=4
The field oscillates much faster than the Universe expands
Equation of state
For p=2
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End of Inflation (III)
The previous model cannot describe particle creation
Γ is the inflaton decay rate
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End of Inflation (IV)
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Reheating era
Oscillatory phase
Radiation-dominated era Matter –dominated era
p=2 p=4
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Reheating era (II)
So far we do not know so much on the reheating temperature, ie (can be (improved – the upper bound- if gravitinos production is taken into account)
end<reh<BBN
The previous description is a naive description of the infaton/rest of the world coupling. It can be much more complicated.
Theory of preheating, thermalization etc …
How does the reheating affect the inflationary predictions?
It modifies the relation between the physical scales now and the number of e-folds at which perturbations left the Hubble radius
Can the oscillations of the inflaton affect the behaviour of the perturbations?
Consequences of reheating
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Probing the reheating with CMB observations
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Inflationary Observables
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Parameterizing the Reheating (I)
Oscillatory phase
p=2 p=4
One needs two numbers, the mean equation of state and the energy density at reheating.
In fact, for the calculations of the perturbation power spectrum, one number is enough, the reheating parameter
Describing the reheating
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The reheating epoch can be described with a single parameter, the so-called reheating parameter; it appears naturally in the equation controlling the evolution of the perturbations
Parameterizing the Reheating (II)
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- Either one uses the constraint on the energy density at the end of reheating to constrain N*
If we are given a model, then the reheating epoch is constrained
- Or we consider Rrad as a new free parameter and we try to constrain it using Bayesian techniques
Parameterizing the Reheating (III)
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Constraining the reheating (I)
Large field inflation
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Large field inflation
Constraining the reheating (II)
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Small field inflation
Constraining the reheating (III)
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Small field inflation
Constraining the reheating (IV)
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Small field inflation
Constraining the reheating (V)
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Large field inflation
Constraining the reheating (VI)
Mean likelihoodsMarginalized posterior probability distributions
(flat prior) p2 [0.2,5]
Flat prior:
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Large field inflation
Constraining the reheating (VII)
(flat prior) p2 [1,5]
(flat prior) reh 2 [nuc,end]
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Small field inflation
Constraining the reheating (VIII)
(flat prior) p2 [2.4,10]
(flat prior) ln(/MPl) 2 [-1,2]
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Small field inflation
wreh=0_
wreh=-0.1_
wreh=-0.2_
wreh=-0.3_
Constraining the reheating (IX)
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Probing the reheating with Gravitational Waves Observations
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Cosmological Perturbations
Oscillatory phase
p=2 p=4
The cosmological perturbations are described by the quantity (curvature perturbation)
The Mukhanov variable obeys the equation of a parametric oscillator
The power spectrum is directly linked to CMB anisotropy
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CMB window 1st order sr
2nd order sr
Exact (numerical)
Inflationary Power Spectrum
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Are perturbations affected by (pre)heating?
Equation of motion during preheating
Mathieu Equation
with
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Are perturbations affected by (pre)heating?
stable
unstable
Mathieu Instablity Card
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Are perturbations affected by (pre)heating?
stable
unstable
Mathieu Instablity Card
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Resonance band
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Are perturbations affected by (pre)heating?
Solution: Floquet theory
Constant curvature perturbation
Early structure formation
μ=q/2 is the Floquet index
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Solution in the resonance band
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Haloes Formation
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no
Non-linearities become important
Virialization
Inflaton halo evaporation
Linear radius
Haloes Formation (II)
A halo of mass M collapses when
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GW Emission
At virialization, the halo emits GW with a frequency
Dynamical timescale at collapse ( is the density of the halo at collapse)
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GW Emission (II)
Energy density energy emitted during the collapse of perturbations corresponding to mass between M and M+dM
Number density of halos of massbetween M and M+dM
Luminosity
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Gravitational Waves Production (II)
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Gravitational Waves Production (III)
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Conclusions
Reheating can affect the inflationary predictions
The reheating temperature can be constrained with the CMB Observations; one obtains a lower bound.
Preheating can affect the perturbations on small scales, even in the single field slow-roll case
Production of gravitational waves; potentially observable
Production of black holes?
Many things remain to be studied
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