Cosmological bounces in spatially flat FRW spacetimes in metric f(R) gravity

TL;DR

This paper investigates conditions for cosmological bounces in spatially flat FRW spacetimes within f(R) gravity, highlighting differences between Jordan and Einstein frames and analyzing scalar perturbations.

Contribution

It introduces a method to analyze bouncing solutions in f(R) gravity using an effective Einstein frame, clarifying the relation between bounces in different frames.

Findings

A bounce in f(R) gravity may not correspond to a bounce in Einstein frame.

The Einstein frame analysis simplifies understanding bounce dynamics.

Scalar perturbation theory in bouncing f(R) models is developed.

Abstract

The present work analyzes the various conditions in which there can be a bouncing universe solution in f(R) gravity. In the article an interesting method, to analyze the bouncing FRW solutions in a spatially flat universe using f(R) gravity models using an effective Einstein frame description of the process, is presented. The analysis shows that a cosmological bounce in the f(R) theory need not be described by an equivalent bounce in the Einstein frame description of the process where actually there may be no bounce at all. Nevertheless the Einstein frame description of the bouncing phenomena turns out to be immensely important as the dynamics of the bounce becomes amenable to logic based on general relativistic intuition. The theory of scalar cosmological perturbations in the bouncing universe models in $f(R)$ theories has also been worked out in the Einstein frame.