Generalized entropies and corresponding holographic dark energy models

H Moradpour,A H Ziaie,M Kord Zangeneh

doi:10.1140/epjc/s10052-020-8307-x

Abstract

Using Tsallis statistics and its relation with Boltzmann entropy, the Tsallis entropy content of black holes is achieved, a result in full agreement with a recent study (Mejrhit and Ennadifi in Phys Lett B 794:24, 2019). In addition, employing Kaniadakis statistics and its relation with that of Tsallis, the Kaniadakis entropy of black holes is obtained. The Sharma-Mittal and Rényi entropy contents of black holes are also addressed by employing their relations with Tsallis entropy. Thereinafter, relying on the holographic dark energy hypothesis and the obtained entropies, two new holographic dark energy models are introduced and their implications on the dynamics of a flat FRW universe are studied when there is also a pressureless fluid in background. In our setup, the apparent horizon is considered as the IR cutoff, and there is not any mutual interaction between the cosmic fluids. The results indicate that the obtained cosmological models have (i) notable powers to describe the cosmic evolution from the matter-dominated era to the current accelerating universe, and (ii) suitable predictions for the universe age.

Highlights

Bekenstein entropy [25] is the cornerstone of primary holographic dark energy hypothesis (PHDE) [28], a promising approach to understand the origin of dark energy
While apparent horizon is a proper causal boundary for cosmos meeting conservation and thermodynamics laws [30,31,32,33,34,35], PHDE with apparent horizon as IR cutoff suffers from some weaknesses [28,29]
Three generalized entropy based holographic dark energy models have been proposed that can provide considerable descriptions for the universe expansion even if apparent horizon is employed as IR cutoff [17,18,19,36]

Summary

Introduction

Bekenstein entropy [25] (and the nature of degrees of freedom of horizon [26,27]) is the cornerstone of primary holographic dark energy hypothesis (PHDE) [28], a promising approach to understand the origin of dark energy. Three generalized entropy based holographic dark energy models have been proposed that can provide considerable descriptions for the universe expansion even if apparent horizon is employed as IR cutoff [17,18,19,36]. Motivated by the above arguments, we are going to (i) calculate the entropy of black holes in the various well-known generalized entropy formalisms, and (ii) study their ability in describing the current accelerated universe by building their corresponding holographic dark energy models in the unit of kB = G = c = h = 1. After addressing relation between Tsallis and Boltzmann entropies, Tsallis entropy of black holes is derived, a result compatible with that of Ref.

Tsallis and Kaniadakis entropies of black holes

New Tsallis Holographic dark energy

The Universe age

Concluding remarks