Probing the Reheating with Astrophysical Observations

1. Probing the Reheating with Astrophysical Observations Jérôme Martin Institut d’Astrophysique de Paris (IAP) [In collaboration with K. Jedamzik & M. Lemoine, arXiv:1002.3039, arXiv:1002.3278 and C. Ringeval, arXiv:1004.5525]

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. 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 • Flatnessproblem • Monopoles problem … Usually +3p>0 (eg p=0) and the expansion is decelerated. Inflation requires negative pressure

4. 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

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

6. End of Inflation (II) Oscillatory phase p=4 p=2 • 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 p=4 p=2 Matter –dominated era Radiation-dominated era

10. 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) • 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?

11. Probing the reheatingwith CMB observations

12. Inflationary Observables

13. Parameterizing the Reheating (I) Oscillatory phase Describing the reheating p=4 p=2 • 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

14. 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

15. 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

16. Constraining the reheating (I) Large field inflation

17. Constraining the reheating (II) Large field inflation

18. Constraining the reheating (III) Small field inflation

19. Constraining the reheating (IV) Small field inflation

20. Constraining the reheating (V) Small field inflation

21. Constraining the reheating (VI) Large field inflation Marginalized posterior probability distributions Mean likelihoods (flat prior) p2 [0.2,5] Flat prior:

22. Constraining the reheating (VII) Large field inflation (flat prior) p2 [1,5] (flat prior) reh 2 [nuc,end]

23. Constraining the reheating (VIII) Small field inflation (flat prior) p2 [2.4,10] (flat prior) ln(/MPl) 2 [-1,2]

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

25. Probing the reheatingwithGravitational Waves Observations

26. 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 p=4 p=2

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

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

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

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

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

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