Dynamical Backreaction in Robertson-Walker Spacetime

TL;DR

This paper investigates the backreaction effects of a quantized scalar field on the evolution of a spatially flat Robertson-Walker universe by deriving the coupled dynamical equations and performing explicit renormalization of the stress tensor.

Contribution

It provides a detailed derivation of the semiclassical Einstein equations with a renormalized stress tensor for a scalar field in Robertson-Walker spacetime, including conformal and general coupling cases.

Findings

Explicit renormalization of the stress tensor in Robertson-Walker spacetime.

Derivation of the coupled dynamical system for the scale factor and scalar field.

Analysis applicable to conformal and non-conformal couplings.

Abstract

The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson-Walker space time. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the sigularities of the stress tensor restricted to equal times in agreement with the usual renormalization prescription for Hadamard states to perform an explicit renormalization. The dynamical system for the Robertson Walker scale parameter $a(t)$ coupled to the scalar field is finally derived for the case of conformal and also general coupling.