Stochastic semiclassical cosmological models

TL;DR

This paper develops a stochastic semiclassical model of the early universe's spacetime, incorporating quantum fluctuations of matter fields via an Einstein-Langevin equation, to better understand metric fluctuations during cosmological evolution.

Contribution

It introduces a stochastic approach to semiclassical gravity using the Einstein-Langevin equation, accounting for quantum matter fluctuations in early universe cosmology.

Findings

Analysis of conformal fluctuations in flat spacetime.

Study of scale factor fluctuations in a simple cosmological model.

Application of stochastic methods to quantum matter-induced metric fluctuations.

Abstract

We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless non-conformal matter fields in the Early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological modelintroduced by Hartle, which consists of a spatially flat isotropic cosmology driven by radiation and dust.