FRW Viscous Dark Fluid with Non-linear Inhomogeneous Equation of State

Abstract

In this paper, we considered a bulk viscosity described by non-linear inhomogeneous equation of state of the type \(p=\omega(\rho)+f(\rho)+\Lambda(H)\), where \(\omega(\rho)=b_{0}\rho^{\delta-1}-1\), \(f(\rho)=A \rho^{\alpha}\) and \(\Lambda(H)= \Lambda_{0}H\). We assume the bulk viscosity as a linear combination of two terms of the form \(\zeta=\zeta_{0}+\zeta_{1}H\) i.e. one is constant and the other is proportional to Hubble parameter \(H\). In the first part of the paper we find the solution of the field equations in terms of time-dependent dark energy density \(\rho\), Hubble parameter \(H\), scale factor \(a\) and also obtain the transition from non-phantom era to the phantom era by using exponential function method. In the second part of the paper, we again find the solutions of the field equations by using the simple integration method and again obtain \(\rho\), \(H\), and \(a\) for the particular case. Finally, we discuss the stability of the model.