Massive gravity: nonlinear instability of the homogeneous and isotropic universe

TL;DR

This paper demonstrates that all homogeneous and isotropic solutions in nonlinear massive gravity are inherently unstable due to the presence of ghost modes that cannot be removed, especially in the large-scale limit.

Contribution

It provides a detailed analysis of the propagating modes on a Bianchi type--I background, revealing the universal instability of isotropic solutions in nonlinear massive gravity.

Findings

All isotropic solutions contain ghost modes.

Ghost frequencies vanish at large scales.

Homogeneous and isotropic solutions are nonlinearly unstable.

Abstract

We argue that all homogeneous and isotropic solutions in nonlinear massive gravity are unstable. For this purpose, we study the propagating modes on a Bianchi type--I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. This ghost mode is interpreted as a leading nonlinear perturbation around a homogeneous and isotropic background.