THDE models with specific cutoffs and correspondence with quintessence field

Abstract

In this paper, we investigated the general behaviors of the Tsallic holographic dark energy (THDE) model in general relativity. Here, we take the Bianchi [Formula: see text] 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 [Formula: see text], matter-energy density [Formula: see text], and skewness parameter [Formula: see text] 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 [Formula: see text]. In addition, we develop the cosmographic parameters like, deceleration parameter [Formula: see text], jerk parameter [Formula: see text], lerk parameter [Formula: see text], snap parameter [Formula: see text] and maxout parameter [Formula: see text]. We have explored the [Formula: see text] 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.