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Probing the cosmological viability of non-gaussian statistics

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 change the strength of the gravitational constant. In this paper, we consider the $w$CDM 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 use type Ia supernovae, baryon acoustic oscillations, Hubble expansion rate function and the linear growth of matter density perturbations data.