Holographic dark energy through Tsallis entropy

Abstract

In order to apply holography and entropy relations to the whole universe, which is a gravitational and thus nonextensive system, for consistency one should use the generalized definition for the universe horizon entropy, namely Tsallis nonextensive entropy. We formulate Tsallis holographic dark energy, which is a generalization of standard holographic dark energy quantified by a new dimensionless parameter δ, possessing the latter as a particular sub-case. We provide a simple differential equation for the dark energy density parameter, as well as an analytical expression for its equation-of-state parameter. In this scenario the universe exhibits the usual thermal history, namely the successive sequence of matter and dark-energy epochs, before resulting in a complete dark energy domination in the far future. Additionally, the dark energy equation-of-state parameter presents a rich behavior and, according to the value of δ, it can be quintessence-like, phantom-like, or experience the phantom-divide crossing before or after the present time. Finally, we confront the scenario with Supernovae type Ia and Hubble parameter observational data, and we show that the agreement is very good, with δ preferring a value slightly larger than its standard value 1. 95.36.+x, 04.50.Kd

Modified cosmology from extended entropy with varying exponent

“…Recently, there have appeared some works in the literature in which the above thermodynamical consideration is applied using extended entropy relations instead of the usual one [36][37][38][39][40][41][42][43][44][45][46]. In particular, it is known that in the case of non-additive systems, such as gravitational ones, the standard Boltzmann-Gibbs additive entropy should be generalized to the non-extensive Tsallis entropy [47][48][49], which can be applied in all cases, possessing the former as a limit.…”

Note on Tsallis holographic dark energy

“…In fact, in a noninteracting universe, while SMHDE is classically stable whenever SMHDE is dominant in the universe, THDE, built using the Tsallis generalized entropy [78], is never stable at the classical level [1,64]. It is also worth mentioning that a THDE model whose IR cutoff is the future event horizon has been studied in a noninteracting universe showing satisfactory results [79].…”

Quintessential Inflation with Dynamical Higgs Generation as an Affine Gravity

“…where the parameters are naturally identified as: (30) in terms of the electro-weak energy scale M EW ∼ 10 −16 M Pl . • Thus, the residual cosmological constant Λ 0 in (28) has to be identified with the current epoch observable cosmological constant (∼ 10 −122 M 4 Pl ) and, therefore, according to (27) the integration constants M 1,2 are naturally identified by orders of magnitude as…”

“…With the discovery of the accelerating expansion of the present universe [27][28][29][30][31][32][33][34][35] it appears plausible that a small vacuum energy density, usually referred in this case as "dark energy", is also present even today. The two vacuum energy densities -the one of inflation and the other of the dark energy dominated universe nowadays, have however a totally different scale which demans a plausible explanation of how cosmological evolution may naturally interpolate between such two apparently quite distinctive physical situations.…”