Out-of-equilibrium evolution of scalar fields in FRW cosmology: renormalization and numerical simulations

TL;DR

This paper develops a covariant, renormalized computational framework for simulating the out-of-equilibrium evolution of a self-interacting scalar field and its quantum fluctuations in an expanding universe, including back reactions.

Contribution

It introduces a novel, covariant renormalization method for scalar fields in FRW cosmology, incorporating quantum and classical back reactions with improved initial state handling.

Findings

Successfully implemented numerical simulations of scalar field evolution during preheating.

Corrected previous issues in energy-momentum tensor renormalization.

Demonstrated the impact of quantum fluctuations on cosmic scale factor dynamics.

Abstract

We present a renormalized computational framework for the evolution of a self-interacting scalar field (inflaton) and its quantum fluctuations in an 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., we consider the the dynamical evolution of the cosmic scale factor. We perform, in the one-loop and in the large-N approximation, 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 counter terms 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 occurence 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.