Stable FLRW solutions in Generalized Massive Gravity

TL;DR

This paper introduces exact FLRW solutions in a generalized massive gravity framework where mass parameters depend on Stuckelberg fields, enabling stable, self-accelerating cosmologies without extra degrees of freedom.

Contribution

It presents a novel class of FLRW solutions in generalized massive gravity with Lorentz-invariant mass functions, ensuring stability and the presence of an active Vainshtein mechanism.

Findings

Existence of exact, self-accelerating FLRW solutions.

Stable solutions free of ghosts and gradient instabilities.

Confirmation of the Vainshtein mechanism via decoupling limit analysis.

Abstract

We present exact FLRW solutions in generalized massive gravity where the mass parameters are naturally promoted to Lorentz-invariant functions of the Stuckelberg fields. This new dependence relaxes the constraint that would otherwise prevent massive gravity from possessing exact FLRW solutions. It does so without the need to introduce additional degrees of freedom. We find self-accelerating cosmological solutions and show that, with a mild restriction on the region of phase space, these cosmological solutions exhibit full stability, i.e. absence of ghosts and gradient instabilities for all the tensor, vector and scalar modes, for all cosmic time. We perform the full decoupling limit analysis, including vector degrees of freedom, which can be used to confirm the existence of an active Vainshtein mechanism about these solutions.