Dark energy model with variable $q$ and $\omega$ in LRS Bianchi-II space-time

The present study deals with spatial homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi-II dark energy model in general relativity. The Einstein’s field equations have been solved exactly by taking into account the proportionality relation between one of the components of shear scalar $({\sigma }_1^1)$ and expansion scalar $(\vartheta )$, which, for some suitable choices of problem parameters, yields time dependent equation of state (EoS) and deceleration parameter (DP), representing a model which generates a transition of universe from early decelerating phase to present accelerating phase. The physical and geometrical behavior of universe have been discussed in detail.