Dynamics of f(R)-cosmologies containing Einstein static models

TL;DR

This paper investigates the dynamics of homogeneous isotropic FRW cosmologies in $f(R)$-gravity, focusing on Einstein static models, their stability, and phenomena like bounces, revealing behaviors absent in General Relativity.

Contribution

It constructs a compact state space for $f(R)=R^n$ models, identifies attractors, and explores bouncing cosmologies, extending understanding beyond classical General Relativity.

Findings

Existence of Einstein static models in $f(R)=R^n$ theories.

Identification of past and future attractors including accelerating models.

Discovery of universes with both past and future bounces, not present in GR.

Abstract

We study the dynamics of homogeneous isotropic FRW cosmologies with positive spatial curvature in $f(R)$-gravity, paying special attention to the existence of Einstein static models and only study forms of $f(R)=R^n$ for which these static models have been shown to exist. We construct a compact state space and identify past and future attractors of the system and recover a previously discovered future attractor corresponding to an expanding accelerating model. We also discuss the existence of universes which have both a past and future bounce, a phenomenon which is absent in General Relativity.