Abstract
This paper deals with the general class of Bianchi cosmological models with varying equation of state (EoS) parameter. We have discussed three different types of physically viable cosmological solutions of average scale factor by using a special law for deceleration parameter which is linear in time with a negative slope. The exact solutions to the corresponding field equations are obtained for three different physical viable cosmologies. The EoS parameter for deceleration parameter as well as dark energy is found to be the time varying function. We have using the latest observational data to draw a qualitative picture of the evaluation of the universe. In our constructed model, the equation of state parameter of dark energy is obtained as time varying and it is evolving with negative sign which is consistent with recent observation. We also shows that, at the early stage, the equation of state (EoS) parameter (γ) is positive i.e. the universe was matter dominated but at large time, the universe evolving with negative values i.e. the present epoch. All physical parameters are calculated and discussed in each physical viable cosmological model.
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