  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.
