Vacua and instantons of ghost-free massive gravity

TL;DR

This paper reviews the vacuum structure and stability of ghost-free massive gravity and bigravity models, highlighting the challenges in connecting different vacua via instantons without violating fundamental energy conditions.

Contribution

It provides a comprehensive analysis of the vacuum solutions and their perturbative stability in dRGT and HR bigravity, and demonstrates the impossibility of regular instantons connecting stable vacua.

Findings

Some self-accelerating vacua contain strongly coupled modes.

Regular instantons connecting stable vacua cannot be constructed without energy condition violations.

Vacuum structure is rich and complex, with stability properties dependent on the model.

Abstract

Recently discovered models of ghost-free massive gravity and bigravity are characterized by a non-trivial potential that gives rise to a rich vacuum structure. We review maximally symmetric vacua of the de Rham-Gabadadze-Tolley (dRGT) massive gravity and of the Hassan-Rosen (HR) bigravity, and discuss their perturbative stability. In particular, we discuss perturbations about self-accelerating vacua in HR bigravity, and argue that, analogously to what was found in the case of dRGT gravity, some of them contain strongly coupled modes. We then show that it is impossible to construct regular instantons connecting different classically stable vacua of dRGT gravity without violating energy conservation or the null energy condition.