1. Zeldovich-90, 21.12.04 1 Prethermalization in early Universe D. Podolsky, G. Felder, L. Kofman, M. Peloso CITA (Toronto), Landau ITP (Moscow), University of Minnesota Sharp change of equation of state from non-relativistic to relativistic: reheating Prethermalization: soon after the end of reheating spectrum is close to thermal at interesting energy scales “ Intermediate” regime of expansion: effective equation of state w=1/4, due to non-trivial time dependence of effective masses What happens between reheating and radiation dominated stage?

2. 2Zeldovich-90, 21.12.04

3. 3 Setup End of inflationary stage φ – inflaton, χ – matter field, m~10 M -6 P

4. 4Zeldovich-90, 21.12.04 Reheating In terms of equation of motion for modes of matter field is, number density Driving parameter is Resonance structure for k=0 in flat spacetime There are growing solutions at some k (param. resonance): At large q, instability zones overlap

5. 5Zeldovich-90, 21.12.04 Prethermalization: results of numerical simulations 1. Effective equation of state w = p/ε Corresp. regime of expansion is 1.Sharp change of equation of state 2.Moment of transition is non-monotonic function of g 2

6. 6Zeldovich-90, 21.12.04 2. Various components of energy density (why particle description is valid), g =2.5 10 2. -7

7. 7Zeldovich-90, 21.12.04 3. Total (comoving) number densities

8. 8Zeldovich-90, 21.12.04 4. Energy densities per mode k Various curves correspond to various moments of time, separation is Δt = 4π/m; curve in the box is Rayleigh spectrum k³, corresponding to

9. 9Zeldovich-90, 21.12.04 5. Spectra of number densities (in log scale) Direct cascade – possibly, this regime can be described in terms of weak turbulence (Tkachev, Micha (2004), KP (work in progress)) Tendency for creation of χ-condensate Prethermalization – at interesting scales spectrum is close to thermal soon enough after the end of reheating

10. 10Zeldovich-90, 21.12.04 6. Means and variances g²=2.5 10g²=10 Variances can be estimated as and They are trivially related with effective masses (Hartree approx.): and -7. -5

11. 11Zeldovich-90, 21.12.04 7. Intermediate regime of expansion: kinematic explanation Contributions of particles into energy density may be estimated as Variances are: and Since number densities are slow functions of time, one has 0-0 component of Einstein equations gives i.e., w=1/4 in the beginning of evolution Physical reason is non-trivial change of effective masses with time in expanding Universe

12. 12Zeldovich-90, 21.12.04 Conclusions Sharp change of equation of state due to preheating Prethermalization – soon after the end of reheating spectrum is close to thermal at all physically interesting scales Numerics Kinematics Intermediate regime of expansion after reheating, corresponds to effective equation of state w ≈ ¼. Explanation: non-trivial dependence of effective masses on time in expanding universe Kinetics Much work to be done – turbulent thermalization of quantum scalar fields, relation to weak turbulence theory (in preparation, 2005)

13. 13Zeldovich-90, 21.12.04 Notes 1. Instability bands for Mathieu equation:, 2. Moment of transition as function of coupling g: