Quantum evolution of scalar fields in Robertson-Walker space-time

TL;DR

This paper investigates the quantum evolution of scalar fields in an expanding universe using a Gaussian approximation within the functional Schrödinger picture, demonstrating renormalizability and finite energy-momentum tensor.

Contribution

It introduces a Gaussian approximation method for scalar field evolution in Robertson-Walker space-time and proves its renormalizability and finiteness of physical quantities.

Findings

Gaussian approximation is renormalizable in this setting

Energy-momentum tensor remains finite after renormalization

Method provides a consistent framework for quantum scalar fields in cosmology

Abstract

We study the $\lambda \phi^4$ field theory in a flat Robertson-Walker space-time using the functional Sch\"odinger picture. We introduce a simple Gaussian approximation to analyze the time evolution of pure states and we establish the renormalizability of the approximation. We also show that the energy-momentum tensor in this approximation is finite once we consider the usual mass and coupling constant renormalizations.