Perturbations in Massive Gravity Cosmology

TL;DR

This paper investigates cosmological perturbations in a ghost-free massive gravity theory with two solution branches, revealing stability issues in one branch and potential resolutions involving mirror dark matter.

Contribution

It analyzes perturbations in a massive gravity model with two branches, identifying stability properties and proposing a dark matter sector to mitigate instabilities.

Findings

First branch shows no extra degrees of freedom at linear level.

Second branch exhibits scalar instabilities on sub-horizon scales.

De Sitter background remains stable with no instabilities.

Abstract

We study cosmological perturbations for a ghost free massive gravity theory formulated with a dynamical extra metric that is needed to massive deform GR. In this formulation FRW background solutions fall in two branches. In the dynamics of perturbations around the first branch solutions, no extra degree of freedom with respect to GR ispresent at linearized level, likewise what is found in the Stuckelberg formulation of massive gravity where the extra metric isflat and non dynamical. In the first branch, perturbations are probably strongly coupled. On the contrary, for perturbations around the second branch solutions all expected degrees of freedom propagate. While tensor and vector perturbations of the physical metric that couples with matter follow closely the ones of GR, scalars develop an exponential Jeans-like instability on sub-horizon scales. On the other hand, around a de Sitter background there is no instability. We argue that one could get rid of the instabilities by introducing a mirror dark matter sector minimally coupled to only the second metric.