FLRW viscous cosmological models

In this paper we solve Friedmann equations by considering a universal media as a non-perfect fluid with bulk viscosity and is described by a general "gamma law" equation of state of the form $p= (\gamma -1) \rho + \Lambda(t)$, where the adiabatic parameter $\gamma$ varies with scale factor $R$ of the metric and $\Lambda$ is the time dependent cosmological constant. A unified description of the early evolution of the universe is presented by assuming the bulk viscosity and cosmological parameter in a linear combination of two terms of the form: $\Lambda(t)=\Lambda_{0} + \Lambda_{1}\frac{\dot{R}}{R}$ and $\zeta = \zeta_{0} + \zeta_{1} \frac{\dot{R}}{R}$, where $\Lambda_{0},\;\Lambda_{1},\, \zeta_{0}$ and $ \zeta_{1}$ are constants, in which an inflationary phase is followed by the radiation dominated phase. For this general gamma law equation of state, an entirely integrable dynamical equation to the scale factor $R$ is obtained along with its exact solutions. In this framework we demonstrate that the model can be used to explain the dark energy dominant universe and for a special choice of the parameters we can explain the accelerating expansion of the universe also for two different phases, viz. combination of dark energy and dark matter phase as well as unified dark energy phase. A special physical check has been performed through sound speed constraint to validate the model. At last we obtain a scaling relation between the Hubble parameter with redshift.