One of the so-called viable modified gravities is analyzed. This kind of gravity theories are characterized by a well behavior at local scales, where General Relativity is recovered, while the modified terms become important at the cosmological level
, where the late-time accelerating era is reproduced, and even the inflationary phase. In the present work, the future cosmological evolution for one of these models is studied. A transition to the phantom phase is observed. Furthermore, the scalar-tensor equivalence of f(R) gravity is also considered, which provides important information concerning this kind of models.
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. The present manuscript 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.
Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The
thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.
Modified gravity is one of the most promising candidates for explaining the current accelerating expansion of the Universe, and even its unification with the inflationary epoch. Nevertheless, the wide range of models capable to explain the phenomena
of dark energy, imposes that current research focuses on a more precise study of the possible effects of modified gravity may have on both cosmological and local levels. In this paper, we focus on the analysis of a type of modified gravity, the so-called f(R,G) gravity and we perform a deep analysis on the stability of important cosmological solutions. This not only can help to constrain the form of the gravitational action, but also facilitate a better understanding of the behavior of the perturbations in this class of higher order theories of gravity, which will lead to a more precise analysis of the full spectrum of cosmological perturbations in future.
