Despite the apparent success of the ΛCDM paradigm, several theoretical and epistemological arguments have been put forward as objections against such a simple model of the Universe. The discomfort that Λ has produced in the spirit of some people has led to consider more complicated alternatives, which, is fair to say, none of them is regarded today as a more serious candidate for dark energy (DE) than the cosmological constant Λ. Among these alternatives are the so-called modified theories of gravity (MTG) as opposed to general relativity. It is fair to say, none of them is regarded today as a more serious candidate for dark energy (DE) than the cosmological constant Λ.

The main interest in my research is gravitation, in particular, astrophysical systems where predictions of alternative models can be tested with current observations and also the theoretical analysis that provide such predictions. I dedicate my research, mostly, to the study of modifications of gravity, in particular, the ones coming from geometric modifications like f (R) and additions to higher orders of the curvature invariants into the action, within this frame we have made a proposal that can provides inflation and late-time acceleration. Given that we are performing modifications into the field equations, the consequences of such changes will impact every astrophysical system. We propose to study their consequences in inflation, late-time cosmology, stars, and black holes.