Bounce and stability in the early cosmology with anomaly-induced corrections

TL;DR

This paper investigates the stability of early universe cosmological models with anomaly-induced corrections, focusing on bounce scenarios and the conditions for stable exponential expansion before transitioning to inflation.

Contribution

It extends previous bounce models by analyzing stability with non-zero cosmological constant and background radiation, highlighting conditions for stable expansion after contraction.

Findings

Stability is achievable during the bounce region.

Stable exponential expansion can follow the bounce.

Instability occurs in the distant past of contraction phase.

Abstract

An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential $e$-folds could be very large, before the transition to the unstable version and the beginning of the Starobinsky inflation. Thus, the stable exponential expansion can be seen as a pre-inflationary semiclassical cosmological solution. We explore whether this stable phase could follow after the bounce, subsequent to the contraction of the Universe. Extending the previous consideration of the bounce, we explore both stable expansion and the bounce solutions in the models with non-zero cosmological constant and the presence of background radiation. The critical part of the analysis concerns stability for small perturbations of the Hubble parameter. It is shown that the stability is possible for the variations in the bounce region, but not in the sufficiently distant past in the contraction phase.