Tsallis Holographic Dark Energy Reconsidered

TL;DR

This paper investigates the interacting Tsallis Holographic Dark Energy model with the Granda-Oliveros cutoff, analytically solving for the Hubble parameter, constraining parameters with observational data, and analyzing its dynamical and thermodynamical properties.

Contribution

It provides an analytical solution for the THDE model with GO cutoff, constrains it with observational data, and explores its dynamical stability and thermodynamical consistency.

Findings

Model reproduces $ ext{Λ}$CDM-like behavior without interaction.

Estimated parameters are consistent with observations.

Model exhibits quintessence behavior and ends in a de Sitter phase.

Abstract

We consider the interacting Tsallis Holographic Dark Energy (THDE), with the Granda-Oliveros (GO) scale as the infrared (IR) cutoff, as dynamical vacuum. We analytically solved for the Hubble parameter, in a spatially flat FLRW universe with dark energy and matter as components, and the solution traces the evolutionary path from the prior decelerated to the late accelerated epoch. Without interaction, the model predicts a $\Lambda$CDM like behavior with an effective cosmological constant. We used Pantheon Supernovae type Ia, observational Hubble data (OHD), cosmic microwave background (CMB), and baryon acoustic oscillation (BAO) data to constrain the free parameters of the model. The estimated values of the cosmological parameters were consistent with observational results. We analyzed the behavior of the model using the statefinder and $\omega^\prime_{e}-\omega_{e}$ plane where $\omega_{e}$ and $\omega^\prime_{e}$ corresponds to the effective equation of state and its evolution, respectively. The model shows a quintessence behavior in general, and the model trajectory ends in a point that corresponds to the de Sitter phase. We performed a dynamical analysis of the model, concluding that the prior decelerated and late accelerated phases are unstable and stable equilibria, respectively. We also investigated the thermodynamical nature of the model and found that the generalized second law remains valid in the dynamical vacuum treatment of the model.