Entropic cosmology for Rényi entropy

In entropic cosmology, one can consider several forms of entropy on the horizon of the universe by using an entropic force scenario. In this framework, the horizon of the universe has entropy and temperature. In this study, we derive the entropic force term from the Bekenstein entropy and from the modified Rényi entropy to investigate the entropic cosmology. This will be done by applying the original logarithmic Rényi entropy formula and then using the Bekenstein entropy as a non-extensive Tsallis entropy. Entropic cosmology is obtained by deriving the modified Friedmann, acceleration, and continuity equations from these entropies. We suppose a homogeneous, isotropic, and spatially flat universe, focusing on a single fluid-dominated universe. Surprisingly, both the Rényi entropy, derived from the entropic force model and the standard Λ CDM (Lambda Cold Dark Matter) model predict the same accelerated expansion of the universe. Further, we have combined both of these models, i.e., Rényi and Bekenstein models and our findings show uniform acceleration of the universe as it is the case for the dark energy.