https://doi.org/10.1140/epjp/s13360-022-03169-6
Regular Article
Entropic cosmology for Rényi entropy
1
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
2
National University of Technology, Islamabad, Pakistan
Received:
12
April
2022
Accepted:
7
August
2022
Published online:
26
August
2022
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 
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
