Generalized entropies and corresponding holographic dark energy models
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Regular Article - Theoretical Physics
Generalized entropies and corresponding holographic dark energy models H. Moradpour1,a , A. H. Ziaie1,b , M. Kord Zangeneh2,c 1 2
Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), University of Maragheh, P.O. Box 55136-553, Maragheh, Iran Physics Department, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz 61357-43135, Iran
Received: 29 April 2020 / Accepted: 31 July 2020 © The Author(s) 2020
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.
1 Introduction Originally, Gibbs put forth that systems including long-range interactions may not be extensive [1], a hypothesis which also motivates people to propose various entropy definitions [2– 4]. Recently, such entropies have been employed to model the cosmic evolution in various setups [5–9]. Generalized entropies have also been employed to study black holes [10– 16] and also to build new holographic dark energy models [17–19]. Additionally, it has been shown that such entropies (i) can provide a theoretical basis for the MOND theory [20], (ii) affect the Jeans mass [21], (iii) may be motivated by a e-mail:
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the quantum features of gravity [22,23], and even, (iv) may describe inflation without considering inflaton [24]. Bekenstein entropy [25] (and therefore, 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. While apparent horizon is a proper causal boundary for cosmos meeting conservation and thermodynamics laws [30– 35], PHDE with apparent horizon as IR cutoff suffers from some weaknesses [28,29]. On the other, three generalized entropy based holographic dark energy models have been proposed that can provide considerable descriptions for the
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