Can $f(R)$ gravity isotropize a pre-bounce contracting universe?

TL;DR

This paper investigates whether $f(R)$ gravity can naturally isotropize a contracting universe before a bounce, finding it possible only in specific models and highlighting challenges in connecting contraction phases with bounce viability.

Contribution

The study demonstrates that isotropisation in $f(R)$ gravity is model-dependent, showing it occurs only in certain exponential models and not in common polynomial forms, impacting bouncing cosmology scenarios.

Findings

Isotropisation not possible in $R^n$ and $R+eta R^2$ models.

Isotropisation possible in exponential $f(R)$ models.

Ekpyrotic phase may not satisfy conditions for isotropisation and viability.

Abstract

We address the important issue of isotropisation of a pre-bounce contracting phase in $f(R)$ gravity, which would be relevant to construct any viable nonsingular bouncing scenario in $f(R)$ gravity. The main motivation behind this work is to investigate whether the $f(R)$ gravity, by itself, can isotropise a contracting universe starting initially with small anisotropy without incorporating a super-stiff or non-ideal fluid, that is impossible in general relativity. Considering Bianchi I cosmology and employing a dynamical system analysis, we see that this is not possible for $R^n$ ($n>1$) and $R+\alpha R^2$ ($\alpha>0$) theory, but possible for $\frac{1}{\alpha}e^{\alpha R}$ ($\alpha>0$) theory. On the other hand, if one does not specify an $f(R)$ theory a priori but demands a cosmology smoothly connecting an ekpyrotic contraction phase to a nonsingular bounce, the ekpyrotic phase \emph{may} not fulfil the condition for isotropisation and physically viability simultaneously.