Entropic cosmology for Renyi 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 Renyi entropy to investigate the entropic cosmology. This will be done by applying the original logarithmic Renyi 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 Renyi entropy, derived from the entropic force model and the standard Lambda CDM (Lambda Cold Dark Matter) model predict the same accelerated expansion of the universe. Further, we have combined both of these models, i.e., Renyi and Bekenstein models and our findings show uniform acceleration of the universe as it is the case for the dark energy.

Automated summary

In entropic cosmology, the consideration of various forms of entropy on the universe's horizon is important. By deriving the entropic force term and using different entropy formulas, the modified Friedmann, acceleration, and continuity equations in entropic cosmology are obtained. Surprisingly, both the Renyi entropy and the standard ΛCDM model predict the accelerated expansion of the universe. Furthermore, when combining the Renyi and Bekenstein models, a uniform acceleration of the universe, similar to dark energy, is observed.