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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