Theoretical and observational constraints of viable f (R) theories of gravity

Modified gravity has attracted much attention over the last few years and remains a potential candidate for dark energy. In particular, the so-called viable f(R) gravity theories, which are able to both recover general relativity and produce late-time cosmic acceleration, have been widely studied in recent literature. Nevertheless, extended theories of gravity suffer from several shortcomings which compromise their ability to provide realistic alternatives to the standard cosmological Lambda CDM Concordance model. We address the existence of cosmological singularities and the conditions that guarantee late-time acceleration, assuming reasonable energy conditions for standard matter in the so-called Hu-Sawicki f(R) model, currently among the most widely studied modifications to general relativity. Then using the supernovae Ia Union 2.1 catalogue, we further constrain the free parameters of this model. The combined analysis of both theoretical and observational constraints sheds some light on the viable parameter space of these models and the form of the underlying effective theory of gravity.