Cosmologies of extended massive gravity

We study the background cosmology of two extensions of dRGT massive gravity. The first is variable mass massive gravity, where the fixed graviton mass of dRGT is replaced by the expectation value of a scalar field. We ask whether self-inflation can be driven by the self-accelerated branch of this theory, and we find that, while such solutions can exist for a short period, they cannot be sustained for a cosmologically useful time. Furthermore, we demonstrate that there generally exist future curvature singularities of the "big brake" form in cosmological solutions to these theories. The second extension is the covariant coupling of galileons to massive gravity. We find that, as in pure dRGT gravity, flat FRW solutions do not exist. Open FRW solutions do exist -- they consist of a branch of self-accelerating solutions that are identical to those of dRGT, and a new second branch of solutions which do not appear in dRGT.