Cosmology and perturbations in massive gravity

We study perturbations around some cosmological backgrounds in the dRGT theory of massive gravity. We develop a general formalism to calculate the perturbations around any background. We derive the Lagrangian for fluctuations in the small scale limit, and for the open FRW solution we repeat the analysis around the full background. We find that the perturbations display similar properties: the longitudinal modes of the massive graviton are instantaneous at quadratic level, but they acquire a time-kinetic term at cubic order.