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It is accepted by the majority of scientific community that the Universe iscurrently in an accelerated epoch. In order to explain this shock of late 90's,a lot of dark energy candidates have been proposed. We study in the context off (R) gravity, how some modifications on General Relativity could reproducesuch behavior of the cosmic evolution. It is showed that in general, an f (R)theory can be reconstructed from a non-minimal scalar-tensor theory, where adesired cosmological solution can be achieved. Some viable models are studiedas well as its cosmological evolution, and the possibility that inflationaryepoch is also a result of these fine modifications.

Reconstructing cosmological solutions in F(R) gravity. Towards a unified model of the Universe evolution