Singular Accelerated Evolution in Massive $F(R)$ Bigravity

Abstract: The possibility to have singular accelerated evolution in the context of $F(R)$ bimetric gravity is investigated. Particularly, we study two singular models of cosmological evolution, one of which is a singular modified version of the Starobinsky $R^2$ inflation model. As we demonstrate, for both models in some cases, the slow-roll parameters become singular at the Type IV singularity, a fact that we interpret as a dynamical instability of the theory under study. This dynamically instability may be an indicator of graceful exit from inflation and we thoroughly discuss this scenario and the interpretation of the singular slow-roll parameters. Furthermore, it is demonstrated that for some versions of $F(R)$ bigravity, singular inflation is realized in consistent way so that inflationary indices are compatible with Planck data. Moreover, we study the late-time behavior of the two singular models and we show that the unified description of early and late-time acceleration can be achieved in the context of bimetric $F(R)$ gravity.