A general mass term for bigravity

TL;DR

This paper develops a new formalism for analyzing perturbations in Hassan-Rosen bigravity, revealing a late-time instability in tensor modes when the mass matrix loses positive definiteness.

Contribution

It introduces a general perturbation formalism for bigravity and explicitly computes the mass term in cosmological backgrounds, highlighting stability issues.

Findings

Tensor sector affected by late-time instability

Mass matrix stability depends on background evolution

Formalism applicable to general backgrounds

Abstract

We introduce a new formalism to study perturbations of Hassan-Rosen bigravity theory, around general backgrounds for the two dynamical metrics. In particular, we derive the general expression for the mass term of the perturbations and we explicitly compute it for cosmological settings. We study tensor perturbations in a specific branch of bigravity using this formalism. We show that the tensor sector is affected by a late-time instability, which sets in when the mass matrix is no longer positive definite.