On Instability of Certain Bi-Metric and Massive-Gravity Theories

TL;DR

This paper investigates the classical stability of cosmological solutions in the Hassan-Rosen bi-metric theory, revealing widespread instabilities that challenge its physical viability and discussing potential curvature-based remedies.

Contribution

It provides a detailed stability analysis of Hassan-Rosen bi-metric theory and proposes a method using curvature deformations to address identified instabilities.

Findings

Many cosmological backgrounds are classically unstable in the theory.

The instability questions the physical viability of the Hassan-Rosen and related models.

A potential solution involves curvature-type deformations to stabilize the theory.

Abstract

Stability about cosmological background solutions to the bi-metric Hassan-Rosen theory is studied. The results of this analysis are presented, and it is shown that a large class of cosmological backgrounds is classically unstable. This sets serious doubts on the physical viability of the Hassan-Rosen theory - and in turn also of the de Rham-Gadabaze-Tolley model, to which the mentioned theory is parent. A way to overcome this instability by means of curvature-type deformations is discussed.