Cosmology and perturbations in massive gravity

We study perturbations around some cosmological backgrounds in the de Rham-Gabadadze-Tolley 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 Friedman-Robertson- Walker 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 kinetic term at cubic order.