Bouncing Palatini cosmologies and their perturbations

TL;DR

This paper explores nonsingular bouncing cosmologies in f(R) gravity, establishing conditions for bounces and cyclic evolution, and analyzing perturbation behavior with a focus on divergence issues and smooth evolution criteria.

Contribution

It introduces a formalism for studying perturbations in bouncing f(R) cosmologies and identifies the specific quadratic curvature correction needed for bounces and cyclic behavior.

Findings

Quadratic curvature correction enables bounces in flat universes.

Perturbations often diverge at the bounce, indicating stability issues.

Conditions for smooth perturbation evolution are derived.

Abstract

Nonsingular cosmologies are investigated in the framework of f(R) gravity within the first order formalism. General conditions for bounces in isotropic and homogeneous cosmology are presented. It is shown that only a quadratic curvature correction is needed to predict a bounce in a flat or to describe cyclic evolution in a curved dust-filled universe. Formalism for perturbations in these models is set up. In the simplest cases, the perturbations diverge at the turnover. Conditions to obtain smooth evolution are derived.