Relativistic Turbulence: A Long Way from Preheating to Equilibrium

Abstract

We study, both numerically and analytically, the development of equilibrium after preheating. We show 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. The resulting time for thermalization is long, and temperature at thermalization is low, $T \sim 100$ eV in the simple $\lambda \Phi^4$ inflationary model. Our results allow a straightforward generalization to realistic models.