Abstract:

The currently observed accelerated expansion of the Universe suggests that cosmic flow dynamics is dominated by some unknown form of dark energy characterized by a large negative pressure. This picture comes out when such a new ingredient, beside baryonic and dark matter, is considered as a source in the r.h.s. of the field equations. Essentially, it should be some form of un-clustered, non-zero vacuum energy which, together with (clustered) dark matter, should drive the global cosmic dynamics. Among the proposals to explain the experimental situation, the “concordance model”, addressed as !CDM, gives a reliable snapshot of the today observed Universe according to the CMBR, LSS and SNeIa data, but presents dramatic shortcomings as the “coincidence and cosmological constant problems” which point out its inadequacy to fully trace back the cosmological dynamics. On the other hand, alternative theories of gravity, extending in some way General Relativity, allow to pursue a different approach giving rise to suitable cosmological models where a late-time accelerated expansion can be achieved in several ways. This viewpoint does not require to find out candidates for dark energy and dark matter at fundamental level (they have not been detected up to now), it takes into account only the “observed” ingredients (i.e. gravity, radiation and baryonic matter), but the l.h.s. of the Einstein equations has to be modified. Despite of this modification, it could be in agreement with the spirit of General Relativity since the only request is that the Hilbert-Einstein action should be generalized asking for a gravitational interaction acting, in principle, in different ways at different scales. We survey the landscape of f (R) theories of gravity in their various formulations, which have been used to model the cosmic acceleration as alternatives to dark energy and dark matter. Besides, we take into account the problem of gravitational waves in such theories. We discuss some successes of f (R) -gravity (where f (R) is a generic function of Ricci scalar R ), theoretical and experimental challenges that they face in order to satisfy minimal criteria for viability.