Cosmological evolution, future singularities, Little Rip and Pseudo-Rip in viable f(R) theories and their scalar-tensor counterpart

Modified f(R) gravity is one of the most promising candidates for dark energy, and even for the unification of the whole cosmological evolution, including the inflationary phase. Within this class of theories, the so-called viable modified gravities represent realistic theories that are capable of reproducing late-time acceleration and satisfy strong constraints at local scales, where general relativity is recovered. This paper deals with the analysis of the cosmological evolution for some of these models, which indicates that the evolution may enter into a phantom phase, but the behavior may be asymptotically stable. Furthermore, the scalar-tensor equivalence of f(R) gravity is considered, which provides useful information about the possibility of the occurrence of a future singularity. The so-called Little Rip and Pseudo-Rip are also studied in the framework of this class of modified gravities.