Out-of-equilibrium evolution of scalar fields in FRW cosmology:: Renormalization and numerical simulations -: art. no. 024016

We present a renormalized computational framework for the evolution of a self-interacting scalar field (inflaton) and its quantum fluctuations in a FRW background geometry. We include a coupling of the field to the Ricci scalar with a general coupling parameter xi. We take into account the classical and quantum back reactions, i.e.. Lye consider the dynamical evolution of the cosmic scale factor. We perform, in the one-loop and in large-N approximations, the renormalization of the equation of motion for the inflaton field, and of its energy momentum tensor. Our formalism is based on a perturbative expansion for the mode functions, and uses dimensional regularization. The renormalization procedure is manifestly covariant and the counterterms are independent of the initial state. Some shortcomings in the renormalization of the energy-momentum tensor in an earlier publication are corrected. We avoid the occurrence of initial singularities by constructing a suitable class of initial states. The formalism is implemented numerically and we present some results for the evolution in the post-inflationary preheating era.