# Tsallis holographic model of dark energy: Cosmic behaviour, statefinder analysis and $\omega_D-\omega_D'$ pair in the non-flat universe

## TL;DR

This paper explores the Tsallis holographic dark energy model in a non-flat universe, analyzing its cosmic evolution, statefinder diagnostics, and $\, ext{ extomega}_D- ext{ extomega}_D'$ pair, and compares it with observational data.

## Contribution

It introduces a detailed analysis of the THDE model in a non-flat universe using statefinder and $ extomega_D- extomega_D'$ diagnostics, highlighting its distinct features from other dark energy models.

## Key findings

- The deceleration parameter and equation of state are derived for the THDE model.
- Evolutionary trajectories depend on the Tsallis parameter and spatial curvature.
- The model's features are distinguished from other dark energy frameworks using diagnostic plots.

## Abstract

The paper investigates the Tsallis holographic dark energy (THDE) model in accordance with the apparent horizon as an infrared cut-off, in a non-flat universe. The cosmological evolution of the deceleration parameter and equation of state of THDE model are calculated. The evolutionary trajectories are plotted for the THDE model for distinct values of the Tsallis parameter $\delta$ besides distinct spatial curvature contributions, in the statefinder $(r, s)$ parameter-pairs and $\omega_{D}-\omega^{'}_{D}$ plane, considering the present value of dark energy density parameter $\Omega_{D0} $, $\Omega_{D0}=0.72$, in the light of $WMAP + eCMB + BAO + H_{0}$ observational data. The statefinder and $\omega_{D}-\omega^{'}_{D}$ plane plots specify the feature of the THDE and demonstrate the separation between this framework and other models of dark energy.