Narrow Results

Within the framework of quantum gravity and modified entropy-area formalism, the Tsallis holographic dark energy is an effort to peep into a mysterious content of the Universe, the dark energy, to analyze its nature. The Tsallis parameter $\delta$ provides the main characteristic of the Tsallis holographic dark energy. Opting the value of Tsallis parameter $\delta \le 2$, a quintessence scalar field description of the Tsallis holographic dark energy model can be obtained. In this work, we present this quintessential explanation of the Tsallis holographic dark energy with $\delta \le 2$ and reconstruct the dynamics of the scalar field and the potential of quintessence.

In this paper, we investigated the general behaviors of the Tsallic holographic dark energy (THDE) model in general relativity. Here, we take the Bianchi $V{I}_0$ metric, which is homogeneous and anisotropic. We investigate the THDE models with the Hubble horizon and Granda–Oliveros (GO) cutoffs. We have studied the behavior of a few quantities, such as dark energy density $({\rho }_D,)$, matter-energy density $({\rho }_m)$, and skewness parameter $(\gamma )$ and discuss their physical significances. In our THDE models, the EoS parameter explains the universe’s evolution based on the value of the non-extensive or Tsallis parameter $\delta$. In addition, we develop the cosmographic parameters like, deceleration parameter $(q)$, jerk parameter $(j)$, lerk parameter $(l)$, snap parameter $(S)$ and maxout parameter $(m)$. We have explored the ${\omega }_D-{\omega }_D^{\prime }$ plane and the stability analysis of the THDE model by a perturbation method. We have also constructed a correspondence between the THDE model with quintessence. Some physical and geometrical behaviors of the models are also discussed.