Stability of the Einstein static universe in massive gravity

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 modification 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.