Coupled scalar fields in a flat FRW universe: renormalisation

TL;DR

This paper develops a renormalisation scheme for coupled scalar fields in a flat FRW universe, enabling stable numerical simulations of their non-equilibrium dynamics including quantum backreaction.

Contribution

It introduces a renormalisation method for coupled scalar fields in an expanding universe, combining theoretical analysis with practical numerical implementation.

Findings

Renormalised equations of motion and energy-momentum tensor derived

Stable numerical simulations demonstrated with a hybrid inflation model

Quantum backreaction included in the dynamics

Abstract

We study the non-equilibrium dynamics of a system of coupled scalar fields in a Friedmann-Robertson-Walker (FRW) universe. We consider the evolution of spatially homogeneous "classical" fields and of their quantum fluctuations including the quantum backreaction in the one-loop approximation. We discuss in particular the dimensional regularisation of the coupled system and a special subtraction procedure in order to obtain the renormalised equations of motion and the renormalised energy-momentum tensor and ensure that the energy is well-defined and covariantly conserved. These results represent at the same time a theoretical analysis and a viable scheme for stable numerical simulations. As an example for an application of the general formalism, we present simulations for a hybrid inflationary model.