On the cosmology of massive gravity

TL;DR

This paper reviews cosmological solutions in non-linear massive gravity, highlighting stability issues of homogeneous solutions and exploring modifications like symmetry breaking and extended theories to achieve stable, self-accelerating cosmologies.

Contribution

It analyzes stability problems in massive gravity cosmologies and proposes two approaches—symmetry breaking and theory extension—to find stable solutions.

Findings

Homogeneous and isotropic solutions suffer from ghost instabilities.

Breaking isotropy can lead to stable cosmological solutions.

Varying mass extensions can provide stable regimes, unlike quasi-dilatonic models.

Abstract

We present a review of cosmological solutions in non-linear massive gravity, focusing on the stability of perturbations. Although homogeneous and isotropic solutions have been found, these are now known to suffer from either Higuchi ghost or a new non-linear ghost instability. We discuss two approaches to alleviate this issue. By relaxing the symmetry of the background by e.g. breaking isotropy in the hidden sector, it is possible to accommodate a stable cosmological solution. Alternatively, extending the theory to allow for new dynamical degrees of freedom can also remove the conditions which lead to the instability. As examples for this case, we study the stability of self-accelerating solutions in the quasi-dilatonic extension and generic cosmological solutions in the varying mass extension. While the quasi-dilaton case turns out to be unstable, the varying mass case allows stable regimes of parameters. Viable self-accelerating solutions in the varying mass theory yet remain to be found.