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

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.

11 pages; no figures; This paper is prepaired as a Proceedings for the International Conference on Holography, String Theory and Discrete Approaches in Hanoi Phenikaa University August 3-8, 2020 Hanoi, Vietnam; Submission to SciPost at: https://scipost.org/SciPostPhysProc.202007001; Presented in the conference on 8/8/2020