Nonlinear stability of cosmological solutions in massive gravity

TL;DR

This paper studies the nonlinear stability of different cosmological solutions in massive gravity, revealing that isotropic solutions are unstable due to ghosts, while anisotropic solutions can be stable under certain conditions.

Contribution

It introduces a method to analyze nonlinear stability of cosmological solutions in massive gravity using perturbation theory around fixed points.

Findings

Isotropic FLRW solutions exhibit nonlinear ghost instability.

Anisotropic FLRW solutions are ghost-free for certain parameters.

The method simplifies nonlinear stability analysis in massive gravity.

Abstract

We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.