On the stability of the Einstein Static Universe in Massive Gravity

TL;DR

This paper investigates the stability of static cosmological solutions in a new massive gravity theory, revealing novel solutions that generalize Einstein's static universe and exhibit varied stability properties.

Contribution

It introduces new static solutions in massive gravity that extend Einstein's universe and analyzes their stability using dynamical systems and numerical methods.

Findings

New static solutions sourced by perfect fluid in massive gravity

Solutions can be neutrally stable or unstable under homogeneous perturbations

Generalizes Einstein Static Universe within a modified gravity framework

Abstract

We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new solutions, only sourced by a perfect fluid, generalizing the Einstein Static Universe found in General Relativity. Using dynamical system techniques and numerical analysis, we show that the found solutions can be either neutrally stable or unstable against spatially homogeneous and isotropic perturbations.