Diapositive 1

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Probing the Reheating with Astrophysical
Observations
Jérôme Martin
Institut dAstrophysique de Paris (IAP)
In collaboration with K. Jedamzik M. Lemoine,
arXiv1002.3039, arXiv1002.3278 and C.
Ringeval, arXiv1004.5525
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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

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Hot Big Bang problems
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 ?3pgt0 (eg p0) and the expansion is
decelerated. Inflation requires negative
pressure
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Inflation in brief
Inflation in a nutshell
Large field

• 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

Hybrid inflation
Small field
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End of Inflation (I)
Oscillatory phase
p4
p2
Slow-roll phase
p4
p2
Violation of Slow-roll
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End of Inflation (II)
Oscillatory phase
p4
p2

• The field oscillates much faster
• than the Universe expands
• Equation of state
• For p2

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End of Inflation (III)

• The previous model cannot describe
• particle creation

• G is the inflaton decay rate

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End of Inflation (IV)
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Reheating era
Oscillatory phase
p4
p2
Matter dominated era
Radiation-dominated era
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Reheating era (II)
Consequences of reheating

• 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)
• 
  ?endlt?rehlt?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

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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
Describing the reheating
p4
p2

• 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

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Parameterizing the Reheating (II)

• 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

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Parameterizing the Reheating (III)
If we are given a model, then the reheating epoch
is constrained
- Either one uses the constraint on the energy
density at the end of reheating to constrain N

• Or we consider Rrad as a new free
• parameter and we try to constrain
• it using Bayesian techniques

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Constraining the reheating (I)
Large field inflation
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Constraining the reheating (II)
Large field inflation
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Constraining the reheating (III)
Small field inflation
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Constraining the reheating (IV)
Small field inflation
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Constraining the reheating (V)
Small field inflation
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Constraining the reheating (VI)
Large field inflation
Marginalized posterior probability distributions
Mean likelihoods
(flat prior) p2 0.2,5
Flat prior
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Constraining the reheating (VII)
Large field inflation
(flat prior) p2 1,5
(flat prior) ?reh 2 ?nuc,?end
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Constraining the reheating (VIII)
Small field inflation
(flat prior) p2 2.4,10
(flat prior) ln(?/MPl) 2 -1,2
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Constraining the reheating (IX)
Small field inflation
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Probing the reheating with Gravitational Waves
Observations
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Cosmological Perturbations
Oscillatory phase

• 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

p4
p2
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Inflationary Power Spectrum
Exact (numerical)
2nd order sr
CMB window
1st order sr
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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?
Mathieu Instablity Card
unstable
stable
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Are perturbations affected by (pre)heating?
Mathieu Instablity Card
unstable
stable
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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

µq/2 is the Floquet index
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Solution in the resonance band
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Haloes Formation
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Haloes Formation (II)
A halo of mass M collapses when
no
Linear radius
Non-linearities become important
Inflaton halo evaporation
Virialization
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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 MdM

Number density of halos of mass between M and MdM
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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