Cosmological model from the holographic equipartition law with a modified R\'{e}nyi entropy

TL;DR

This paper derives a cosmological acceleration equation using a modified Rényi entropy within Padmanabhan's holographic equipartition law, resulting in a constant-like term consistent with the observed cosmological constant.

Contribution

It introduces a novel approach by applying a modified Rényi entropy to derive cosmological equations, linking nonextensive entropy concepts with cosmic acceleration.

Findings

Derivation of an acceleration equation with a constant-like term

The constant-like term's order matches observed cosmological constant

A specific condition constrains the value of the constant-like term

Abstract

Cosmological equations were recently derived by Padmanabhan from the expansion of cosmic space due to the difference between the degrees of freedom on the surface and in the bulk in a region of space. In this study, a modified R\'{e}nyi entropy is applied to Padmanabhan's `holographic equipartition law', by regarding the Bekenstein--Hawking entropy as a nonextensive Tsallis entropy and using a logarithmic formula of the original R\'{e}nyi entropy. Consequently, the acceleration equation including an extra driving term (such as a time-varying cosmological term) can be derived in a homogeneous, isotropic, and spatially flat universe. When a specific condition is mathematically satisfied, the extra driving term is found to be constant-like as if it is a cosmological constant. Interestingly, the order of the constant-like term is naturally consistent with the order of the cosmological constant measured by observations, because the specific condition constrains the value of the constant-like term.