Bouncing cosmologies in massive gravity on de Sitter

In the framework of massive gravity with a de Sitter reference metric, we study homogeneous and isotropic solutions with positive spatial curvature. Remarkably, we find that bounces can occur when cosmological matter satisfies the strong energy condition, in contrast to what happens in classical general relativity. This is due to the presence in the Friedmann equations of additional terms, which depend on the scale factor and its derivatives and can be interpreted as an effective fluid. We present a detailed study of the system using a phase space analysis. After having identified the fixed points of the system and investigated their stability properties, we discuss the cosmological evolution in the global physical phase space. We find that bouncing solutions are generic. Moreover, depending on the solutions, the cosmological evolution can lead to an asymptotic de Sitter regime, a curvature singularity or a determinant singularity.