Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity

TL;DR

This paper analyzes the dynamics of anisotropic cosmologies within $R^n$-gravity using a compact state space approach, identifying equilibrium points, stability, and bouncing solutions, with implications for isotropisation.

Contribution

It introduces a detailed dynamical systems analysis of orthogonal Bianchi cosmologies in $R^n$-gravity, including stability and bouncing solutions, expanding understanding of these models.

Findings

No Einstein static solutions found.

Existence of bouncing cosmological solutions.

All isotropic points are flat Friedmann-like.

Abstract

In this paper we study the dynamics of {\it orthogonal spatially homogeneous} Bianchi cosmologies in $R^n$-gravity. We construct a compact state space by dividing the state space into different sectors. We perform a detailed analysis of the cosmological behaviour in terms of the parameter $n$, determining all the equilibrium points, their stability and corresponding cosmological evolution. In particular, the appropriately compactified state space allows us to investigate static and bouncing solutions. We find no Einstein static solutions, but there do exist cosmologies with bounce behaviours. We also investigate the isotropisation of these models and find that all isotropic points are flat Friedmann like.