Preheating and Thermalization after Inflation

After a short review of inlationary preheating, we discuss the development of equilibrium in the frameworks of massless $\lambda {\mathrm{\Phi }}^4$ model. It is shown that the process is characterised by the appearance of Kolmogorov spectra and the evolution towards thermal equilibrium follows self-similar dynamics. Simplified kinetic theory gives values for all characteristic exponents which are close to what is observed in lattice simulations. This allows estimation of the resulting reheating temperature.