General form of entropy on the horizon of the universe in entropic cosmology

TL;DR

This paper explores how different forms of entropy on the universe's horizon affect energy exchange and consistency of cosmological equations, highlighting the special role of Bekenstein entropy in entropic cosmology.

Contribution

It introduces a general entropic-force model with entropy proportional to the n-th power of the horizon radius, analyzing its impact on the consistency of cosmological equations.

Findings

The model is consistent for Bekenstein entropy (n=2).

Volume and quartic entropies are less consistent with the equations.

Supports the holographic principle through energy exchange scenarios.

Abstract

Entropic cosmology assumes several forms of entropy on the horizon of the universe, where the entropy can be considered to behave as if it were related to the exchange (the transfer) of energy. To discuss this exchangeability, the consistency of the two continuity equations obtained from two different methods is examined, focusing on a homogeneous, isotropic, spatially flat, and matter-dominated universe. The first continuity equation is derived from the first law of thermodynamics, whereas the second equation is from the Friedmann and acceleration equations. To study the influence of forms of entropy on the consistency, a phenomenological entropic-force model is examined, using a general form of entropy proportional to the $n$-th power of the Hubble horizon. In this formulation, the Bekenstein entropy (an area entropy), the Tsallis--Cirto black-hole entropy (a volume entropy), and a quartic entropy are represented by $n=2$, $3$, and $4$, respectively. The two continuity equations for the present model are found to be consistent with each other, especially when $n=2$, i.e., the Bekenstein entropy. The exchange of energy between the bulk (the universe) and the boundary (the horizon of the universe) should be a viable scenario consistent with the holographic principle.