Holographic dark energy through Tsallis entropy

TL;DR

This paper introduces a generalized holographic dark energy model based on Tsallis nonextensive entropy, which allows for a richer range of cosmic behaviors and fits observational data well.

Contribution

It formulates Tsallis holographic dark energy with a new parameter, providing analytical solutions and demonstrating compatibility with observations, extending standard models.

Findings

The universe's thermal history is preserved in the model.

The dark energy equation-of-state can be quintessence-like, phantom-like, or crossing the phantom divide.

The model fits Supernovae and Hubble data well, with a preferred parameter value slightly above 1.

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 $\delta$, 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 $\delta$, 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 $\delta$ preferring a value slightly larger than its standard value 1.