Interacting holographic dark energy in Bianchi type-V and IX universes with variable deceleration parameter

In this paper, we study spatially homogeneous and anisotropic Bianchi type-V and IX universes filled with interacting dark matter and holographic dark energy. We obtained the solution of the field equations by using the variable deceleration parameter in the form [Formula: see text]. The cosmological parameters of the models like deceleration and equation of state are obtained. We observe that the deceleration parameter tends to [Formula: see text] which shows an accelerated universe, and the equation of state tends to [Formula: see text] which belongs to [Formula: see text]CDM model. Moreover, we establish the correspondence between holographic dark energy model and quintessence scalar field.

Variable deceleration parameter and dark energy models

This paper deals with the Bianchi type-III dark energy model and equation of state parameter in a first class of [Formula: see text] gravity. Here, [Formula: see text] and [Formula: see text] represents the Ricci scalar and trace of the energy momentum tensor, respectively. The exact solutions of the modified field equations are obtained by using (i) linear relation between expansion scalar and shear scalar, (ii) linear relation between state parameter and skewness parameter and (iii) variable deceleration parameter. To obtain the physically plausible cosmological models, the variable deceleration parameter with the suitable substitution leads to the scale factor of the form [Formula: see text], where [Formula: see text] and [Formula: see text] are arbitrary constants. It is observed that our models are accelerating for [Formula: see text] and for [Formula: see text], transition phase from deceleration to acceleration. Further, we have discussed physical properties of the models.