Linear stability of semiclassical theories of gravity

TL;DR

This paper studies the stability of semiclassical gravity models by analyzing linear perturbations in a toy model, showing that massive quantum fields can lead to decay of perturbations and stability under certain conditions.

Contribution

It introduces a detailed analysis of linear stability in a semiclassical gravity toy model, highlighting conditions for decay of perturbations and stability.

Findings

Massive quantum fields can stabilize semiclassical solutions.

Linear perturbations decay polynomially over time under certain renormalization.

The model mimics early universe semiclassical Einstein equations.

Abstract

The linearization of semiclassical theories of gravity is investigated in a toy model, consisting of a quantum scalar field in interaction with a second classical scalar field which plays the role of a classical background. This toy model mimics also the evolution induced by semiclassical Einstein equations, such as the one which describes the early universe in the cosmological case. The equations governing the dynamics of linear perturbations around simple exact solutions of this toy model are analyzed by constructing the corresponding retarded fundamental solutions, and by discussing the corresponding initial value problem. It is shown that, if the quantum field which drives the back-reaction to the classical background is massive, then there are choices of the renormalization parameters for which the linear perturbations with compact spatial support decay polynomially in time for large times, thus indicating stability of the underlying semiclassical solution.