Abstract
We consider the dynamics of metric perturbations in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational wave in this theory on the most general homogeneous and isotropic background, and then explore the stability of such background with respect to metric perturbations. 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. The consideration was based on explicit derivation of gravitational wave equations in the theory with anomaly-induced quantum corrections and on the use of both analytical and numerical methods to perform the detailed analysis of these equations. The main conclusion of our work is that the stability conditions are essentially related to the sign of the Weyl-squared term in the classical action of vacuum and do not manifest any essential dependence on the quantum contributions. Furthermore, we analyze the behavior of metric perturbations during inflationary period, in the stable phase of the Modified Starobinsky inflation.
