Abstract
Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there through non-gaussian statistical theories proposed by Tsallis and Kaniadakis. The effect of these non-gaussian statistics in the cosmological context is to change the strength of the gravitational constant. In this paper, we consider the wCDM model modified by the non-gaussian statistics and investigate the compatibility of these non-gaussian modification with the cosmological observations. In order to analyze in which extend the cosmological data constrain these non-extensive statistics, we will use type Ia supernovae, baryon acoustic oscillations, Hubble expansion rate function and the linear growth of matter density perturbations data. We show that Tsallis' statistics is favored at 1σ confidence level.