Gravitational waves and stability of cosmological solutions in the theory with anomaly-induced corrections

TL;DR

This paper investigates the stability of cosmological solutions under metric perturbations in a gravity theory with anomaly-induced quantum corrections, deriving gravitational wave equations and analyzing stability during various cosmological epochs.

Contribution

It derives gravitational wave equations in a quantum-corrected gravity theory and extends stability analysis to radiation, matter, and inflationary cosmologies.

Findings

Stable Minkowski and de Sitter solutions confirmed.

Stability of radiation and matter dominated universes analyzed.

Behavior of perturbations during inflation studied.

Abstract

The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic background, and then verify the stability of such background with respect to metric perturbations. The problem under consideration has several interesting applications. Our first purpose is to explore the stability of the classical cosmological solutions in the theory with quantum effects taken into account. There is an interesting literature about stability of Minkowski and de Sitter spaces and here we extend the consideration also to the radiation and matter dominated cosmologies. Furthermore, we analyze the behavior of metric perturbations during inflationary period, in the stable phase of the Modified Starobinsky inflation.