Stability of the Einstein static universe in f(R) gravity

TL;DR

This paper investigates the stability of the Einstein static universe within f(R) gravity, revealing that certain modifications can stabilize solutions that are unstable in classical general relativity.

Contribution

It demonstrates that f(R) gravity can stabilize the Einstein static universe under specific conditions, unlike in general relativity.

Findings

Stable Einstein static universe exists in f(R) gravity with positive cosmological constant.

Stability regions depend on the equation of state parameter w.

Modifications in f(R) gravity can stabilize solutions unstable in general relativity.

Abstract

We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are parameterized by a linear equation of state parameter w=p/rho. Contrary to classical general relativity, it is found that in f(R) gravity a stable Einstein cosmos with a positive cosmological constant does indeed exist. Thus, we are lead to conclude that, in principle, modifications in f(R) gravity stabilize solutions which are unstable in general relativity.