Probing the Reheating with Astrophysical Observations Jérôme Martin Institut d’Astrophysique de Paris (IAP) 1 [In collaboration with K. Jedamzik & M. Lemoine, arXiv: , arXiv: and C. Ringeval, arXiv: ]

2 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

3 07/10/2015 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

4  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

5 End of Inflation (I) Slow-roll phase Oscillatory phase p=2 p=4 p=2 p=4 Violation of Slow-roll

6 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

7 End of Inflation (III)  The previous model cannot describe particle creation  Γ is the inflaton decay rate

8 End of Inflation (IV)

9 Reheating era Oscillatory phase Radiation-dominated era Matter –dominated era p=2 p=4

10 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

11 Probing the reheating with CMB observations

12 Inflationary Observables

13 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

14  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)

15 - 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 R rad as a new free parameter and we try to constrain it using Bayesian techniques Parameterizing the Reheating (III)

16 Constraining the reheating (I) Large field inflation

17 Large field inflation Constraining the reheating (II)

18 Small field inflation Constraining the reheating (III)

19 Small field inflation Constraining the reheating (IV)

20 Small field inflation Constraining the reheating (V)

21 Large field inflation Constraining the reheating (VI) Mean likelihoods Marginalized posterior probability distributions (flat prior) p 2 [0.2,5] Flat prior:

22 Large field inflation Constraining the reheating (VII) (flat prior) p 2 [1,5] (flat prior)  r eh 2 [  nuc,  end ]

23 Small field inflation Constraining the reheating (VIII) (flat prior) p 2 [2.4,10] (flat prior) ln(  /M Pl ) 2 [-1,2]

24 Small field inflation w reh =0 _ w reh =-0.1 _ w reh =-0.2 _ w reh =-0.3 _ Constraining the reheating (IX)

25 Probing the reheating with Gravitational Waves Observations

26 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

27 CMB window 1st order sr 2nd order sr Exact (numerical) Inflationary Power Spectrum

28 Are perturbations affected by (pre)heating?  Equation of motion during preheating  Mathieu Equation with

29 Are perturbations affected by (pre)heating? stable unstable Mathieu Instablity Card

30 Are perturbations affected by (pre)heating? stable unstable Mathieu Instablity Card

31 Resonance band

32 Are perturbations affected by (pre)heating?  Solution: Floquet theory  Constant curvature perturbation  Early structure formation μ=q/2 is the Floquet index

33 Solution in the resonance band

34 Haloes Formation

35 no Non-linearities become important Virialization Inflaton halo evaporation Linear radius Haloes Formation (II) A halo of mass M collapses when

36 GW Emission  At virialization, the halo emits GW with a frequency Dynamical timescale at collapse ( is the density of the halo at collapse)

37 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 mass between M and M+dM Luminosity

38 Gravitational Waves Production (II)

39 Gravitational Waves Production (III)

40 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

41