Stability of Einstein and de Sitter Universes in the Quadratic Theory of Modified Gravity

TL;DR

This paper investigates the stability of Einstein static and de Sitter universes within a quadratic modified gravity theory, finding the Einstein static universe unstable while the de Sitter universe remains stable under perturbations.

Contribution

It analyzes the stability of key cosmological solutions in a quadratic gravity model, extending understanding of their behavior beyond general relativity.

Findings

Einstein static universe is unstable in quadratic modified gravity.

De Sitter universe remains stable under metric perturbations.

Results highlight differences in stability properties compared to general relativity.

Abstract

We consider the Einstein static and the de Sitter universe solutions and examine their instabilities in a subclass of quadratic modified theories for gravity. This modification proposed by Nash is an attempt to generalize general relativity. Interestingly, we discover that the Einstein static universe is unstable in the context of the modified gravity. In contrast to Einstein static universe, the de Sitter universe remains stable under metric perturbation up to the second order.