SnIa constraints on the event-horizon thermodynamical model of dark energy

Abstract

We apply the thermodynamical model of the cosmological event horizon of the spatially flat FLRW metrics to the study of the recent accelerated expansion phase and to the coincidence problem. This model, called "ehT model" hereafter, led to a dark energy (DE) density Λ varying as r −2 , where r is the proper radius of the event horizon. Recently, another model motivated by the holographic principle gave an independent justification of the same relation between Λ and r. We probe the theoretical results of the ehT model with respect to the SnIa observations and we compare it to the model deduced from the holographic principle, which we call "LHG model" in the following.Our results are in excellent agreement with the observations for H0 = 64kms −1 M pc −1 , and Ω 0 Λ = 0.63 +0.1 −0.01 , which leads to q0 = −0.445 and zT ≃ 0.965.

Cosmological energy in a thermo-horizon and the first law

“…(10), L is strictly increasing in the Q-space (accelerated universe) where 0 < ε < 1. The same result can be derived for the entropy S given by (5).…”

“…ii) Secondly, we can consider the holographic model of the DE (16) compatible with the present observations (acceleration and EoS today ω Λ ≃ −1 [5,6,11]) and modify the first law (4) to be compatible with the chosen model for the DE.…”

“…By a general demonstration independent of the underlying model for the DE, we show in this article a contradiction (except in de Sitter) between the first law introduced in [7,8] for the thermo-horizon that leads to · −E = · R A , and the definition of the total energy in the horizon E = R A 2 . To solve this contradiction, we propose to replace the first law by a Gibbs' equation for the DE component, which is naturally associated to the e.h. in the model [4,5], later supported by an holographic model [6] in an independent approach.…”

“…In section 3, we present the contradiction between the amount of energy derived from the first law and the definition of the energy inside the horizon. We then show that this contradiction is resolved in a thermodynamical model for a DE [4,5] based on the e.h. (Section 4).…”

“…To achieve this goal, we propose a Gibbs' equation describing the thermodynamics of the component DE instead of the first law (4). This approach was introduced in the model [4,5], where a DE component with an energy density of type (16) (with c = 1) and an EoS of vacuum-type were considered…”