Anisotropic cosmological solutions in $R + R^2$ gravity

TL;DR

This paper explores the early universe dynamics in $R+R^2$ gravity, revealing stable anisotropic solutions and their properties near the initial singularity through analytical and numerical methods.

Contribution

It introduces a new two-parameter family of solutions in $R+R^2$ gravity, including stable anisotropic Kasner-like solutions and analyzes their behavior near the singularity.

Findings

Existence of a stable anisotropic Kasner solution.

Analytic description of shear evolution in $f(R)$ gravity.

Asymptotic form of Ricci scalar near the initial singularity.

Abstract

In this paper we investigate the past evolution of an anisotropic Bianchi I universe in $R+R^2$ gravity. Using the dynamical system approach we show that there exists a new two-parameters set of solutions that includes both an isotropic "false radiation" solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behaviour of the shear from a specific property of $f(R)$ gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally we numerically checked our results.