Interacting Tsallis holographic dark energy and tachyon scalar field dark energy model in Bianchi type-II Universe

Abstract

In this work, we study the interaction between the dark matter (DM) component and the dark energy (DE) component using the Tsallis holographic dark energy (THDE) density expression for a Bianchi type-II space–time within the framework of general relativity (GR). To obtain the exact solutions of Einstein’s field equations, we use two constraints: (i) the expansion scalar [Formula: see text] of the Universe is proportional to the component [Formula: see text] of the shear tensor [Formula: see text], i.e. [Formula: see text] and (ii) we assume that the scale factor follows the Hybrid Expansion Law (HEL). We have discussed some geometrical and physical parameters of our model such as the deceleration parameter (DP) and the equation of state (EoS) parameter. In these parameters, we plot their behavior in terms of redshift [Formula: see text]. We observe that the DP evolves from the early decelerating phase to the current accelerating phase with a current value consistent with the observation data. The EoS parameter evolves from a state of a stiff-matter fluid-dominated era [Formula: see text] for high redshift [Formula: see text] to a [Formula: see text]CDM era [Formula: see text] in the later times. Also, we have established a correspondence between the THDE model and the tachyon scalar field dark energy model. We have reconstructed the potential and the tachyon scalar field, which describes the current accelerated expansion of the Universe. Finally, using 51 values of observed Hubble measurement and the technique [Formula: see text]-test, we found the best fit value for the model parameters [Formula: see text], [Formula: see text] and [Formula: see text] (current value of the Hubble parameter). These results are consistent with the new measurements of [Formula: see text].37