Abstract
We investigate the recently proposed holographic dark energy models with the apparent horizon as the IR cutoff by assuming Kaniadakis and generalized Tsallis entropies in the fractal universe. The implications of these models are discussed for both the interacting ( Γ = 3 H b 2 ρ m ) and noninteracting ( b 2 = 0 ) cases through different cosmological parameters. Accelerated expansion of the universe is justified for both models through deceleration parameter q . In this way, the equation of state parameter ω d describes the phantom and quintessence phases of the universe. However, the coincidence parameter r ~ = Ω m / Ω d shows the dark energy- and dark matter-dominated eras for different values of parameters. It is also mentioned here that the squared speed of sound gives the stability of the model except for the interacting case of the generalized Tsallis holographic dark energy model. It is mentioned here that the current dark energy models at the apparent horizon give consistent results with recent observations.
Highlights
To acquire a unified understanding of various entropy measures and how they connect to each other in a generalized form, it is required to recall characteristics of “classical” entropies
Some other holographic dark energy (HDE) models based on generalized entropy can give a considerable description of accelerated expansion of the universe even when the apparent horizon is used as the IR cutoff [12, 13, 27]
A lot of work has been done by Dubey et al [31], Sharma et al [32,33,34], Srivastava et al [35], and Ghaffari et al [17, 36] on cosmic expansion in various theories of gravity by using recently obtained DE models such as new Tsallis HDE (NTHDE), Réyni HDE (RHDE), and Barrow HDE (BHDE)
Summary
To acquire a unified understanding of various entropy measures and how they connect to each other in a generalized form, it is required to recall characteristics of “classical” entropies. A lot of work has been done by Dubey et al [31], Sharma et al [32,33,34], Srivastava et al [35], and Ghaffari et al [17, 36] on cosmic expansion in various theories of gravity by using recently obtained DE models such as new Tsallis HDE (NTHDE), Réyni HDE (RHDE), and Barrow HDE (BHDE) They have made versatile studies on accelerated expansion of the universe through various cosmological parameters and planes and found consistent results with recent Planck’s data [37]. The Kaniadakis statistics have been studied as generalized entropy measures [2, 4] with some gravitational and cosmological consequences [7, 38] In view of these generalized entropies, HDE models have been developed by Moradpour et al [11].
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