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

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 $R+\hat{I}\pm R^2$ ($\hat{I}\pm >0$) theory, but possible for $\frac{1}{\hat{I}}\pm e^{\hat{I}\pm R}$ ($\hat{I}\pm >0$) 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.

35 pages, 4 figures