Cosmological Constraints from Hubble Parameter on F ( R ) Cosmologies

Modified f (R) gravity in the Palatini approach has been presently applied to Cosmology as a realistic alternative to dark energy. In this concern, a number of authors have searched for observational constraints on several f (R) gravity functional forms using mainly data of type Ia supenovae (SNe Ia), Cosmic Microwave Background (CMB) radiation and Large Scale Structure (LSS). In this paper, by considering a homogeneous and isotropic flat universe, we use determinations of the Hubble function H(z), which are based on differential age method, to place bounds on the free parameters of the f (R) = R − β/R n functional form. We also combine the H(z) data with constraints from Baryon Acoustic Oscillations (BAO) and CMB measurements, obtaining ranges of values for n and β in agreement with other independent analyses. We find that, for some intervals of n and β, models based on f (R) = R − β/R n gravity in the Palatini approach, unlike the metric formalism, can produce the sequence of radiation-dominated, matter-dominated, and accelerating periods without need of dark energy. 1. INTRODUCTION Nowadays, one of the key problems at the interface between fundamental physics and cosmology is to understand the physical mechanism behind the late-time acceleration of the Universe. In principle, this phenomenon may be the result of unknown physical processes involving either modifications of gravitation theory or the existence of new fields in high energy physics. Although the latter route is most commonly used, which gives rise to the idea of a dark energy component following the former, at least two other attractive approaches to this problem can be explored. The first one is related to the possible existence of extra dimensions, an idea that links cosmic acceleration with the hierarchy problem in high energy physics, and gives rise to the so-called brane-world cosmol-The second one, known as f (R) gravity, examine the possibility of modifying Einstein's general rela-tivity (GR) by adding terms proportional to powers of the Ricci scalar R to the Einstein-Hilbert La-grangian The cosmological interest in f (R) gravity dates back at least to the early 1980s and arose initially from the fact that these theories may exhibit an early phase of accelerating expansion without introducing new degrees of freedom (Starobinsky 1980). Recently, f (R) gravity began to be thought of as an alternative to dark energy (Capozziello et al. a number of authors have explored their theeoretical and …