Stable Cosmology in Generalised Massive Gravity

TL;DR

This paper analyzes the stability of cosmological perturbations in a generalized massive gravity theory where mass parameters depend on St"uckelberg fields, extending previous models to include all graviton polarizations and ensuring stable accelerated expansion.

Contribution

It introduces a generalized massive gravity framework with variable mass parameters and demonstrates stable cosmological solutions with all graviton polarizations propagating.

Findings

Stable accelerated expansion achieved in the minimal model.

Conditions derived to avoid ghost, gradient, and tachyonic instabilities.

All five graviton polarizations propagate in the extended theory.

Abstract

We present a thorough analysis of the cosmological perturbations in Generalised Massive Gravity. This is an extension of de Rham-Gabadadze-Tolley theory where the translation invariance in the St\"uckelberg field space is broken. This allows the mass parameters to be promoted to functions of the St\"uckelberg fields. We consider an exact cosmological background in this theory and study the stability of perturbations. We derive conditions to avoid ghost, gradient and tachyonic instability. The cosmology is an extension of the self-accelerating branch of the constant mass parameter theory, but now all five massive graviton polarisations propagate. For concreteness, we consider a minimal version of the theory where cosmology undergoes an accelerated expansion at late times and show that the perturbative stability is preserved for a range of parameters.