Singular inflationary universe from F ( R ) gravity

Unlike crushing singularities, the so-called type IV finite time singularity offers the possibility that the Universe passes smoothly it, without any catastrophic effects. Then the question is if the effects of a type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of F(R) gravity. As we demonstrate, the effects of a type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a type IV singularity, with the singularity occurring at the end of inflation. We demonstrate that the toy model has an unstable de Sitter point at the singularity, so indeed graceful exit could be triggered. Finally, we study the late-time dynamics of the toy model and of the singular inflation model and we demonstrate that the unification of early and late-time acceleration can be achieved.