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Modified f(R) gravity is one of the most promising candidates for darkenergy, and even for the unification of the whole cosmological evolution,including the inflationary phase. Within this class of theories, the so-calledviable modified gravities represent realistic theories that are capable ofreproducing late-time acceleration, and satisfy strong constraints at localscales, where General Relativity is recovered. The present manuscript dealswith the analysis of the cosmological evolution for some of these models, whichindicates that the evolution may enter into a phantom phase, but the behaviormay be asymptotically stable. Furthermore, the scalar-tensor equivalence off(R) gravity is considered, which provides useful information about thepossibility of the occurrence of a future singularity. The so-called Little Ripand Pseudo-Rip are also studied in the framework of this class of modifiedgravities.

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