Emergent universe scenario, bouncing universes, and cyclic universes in degenerate massive gravity

We consider alternative inflationary cosmologies in massive gravity with degenerate reference metrics and study the feasibilities of the emergent universe scenario, bouncing universes, and cyclic universes. We focus on the construction of the Einstein static universe, classes of exact solutions of bouncing universes, and cyclic universes in degenerate massive gravity. We further study the stabilities of the Einstein static universe against both homogeneous and inhomogeneous scalar perturbations and give the parameters region for a stable Einstein static universe.