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

It is accepted by the majority of scientific community that the Universe is currently 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 of f(R) gravity, how some modifications on General relativity could reproduce such 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 a desired cosmological solution can be achieved. Some viable models are studied as well as its cosmological evolution, and the possibility that inflationary epoch is also a result of these fine modifications.