Constraining f(R) theories with Type Ia Supernovae and Gamma Ray Bursts

Abstract

Fourth - order gravity theories have received much interest in recent years thanks to their ability to provide an accelerated cosmic expansion in a matter only universe. In these theories, the Lagrangian density of the gravitational field has the form R + f(R), and the explicit choice of the arbitrary function f(R) must meet the local tests of gravity and the constraints from the primordial abundance of the light elements. Two popular classes of f(R) models, which are expected to fulfill all the above requirements, have recently been proposed. However, neither of these models has ever been quantitatively tested against the available astrophysical data. Here, by combining Type Ia Supernovae and Gamma Ray Bursts, we investigate the ability of these models to reproduce the observed Hubble diagram over the redshift range (0, 7). We find that both models fit very well this dataset with the present day values of the matter density and deceleration parameters which agree with previous estimates. However, the strong degeneracy among the f(R) parameters prevents us from putting strong constraints on the values of these parameters; nevertheless, we can identify the regions of the parameter space that should, in principle, be carefully explored with future data and dynamical probes in order to discriminate among f(R) theories and standard dark energy models.