Cosmological constraints from the Hubble parameter on f(R) cosmologies

Modified f(R) gravity in the Palatini approach has been recently applied in cosmology as a realistic alternative to dark energy. In this regard, a number of authors have searched for observational constraints on several f( R) gravity functional forms using mainly data from type Ia supernovae, cosmic microwave background (CMB) radiation and large scale structure. In this paper, considering a homogeneous and isotropic. at universe, we use determinations of the Hubble function H(z), which are based on a differential age method, to place bounds on the free parameters of the f( R) = R- beta/R-n functional form. We also combine the H(z) data with constraints from baryon acoustic oscillations and CMB measurements, obtaining ranges of values for n and beta in agreement with other independent analyses. We find that, for some intervals of n and beta, models based on f(R) = R- beta/R-n gravity in the Palatini approach, unlike the metric formalism, can produce a sequence of radiation-dominated, matter-dominated, and accelerating periods without the need for dark energy.