Friedmann Cosmology with a Generalized Equation of State and Bulk Viscosity

The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state (endowed some deviation from the conventionally assumed cosmic perfect fluid model). We assume the bulk viscosity is a linear combination of two terms: one is constant, and the other is proportional to the scalar expansion θ = 3ȧ/a. The equation of state is described as p = (γ−1)ρ+p0, where p0 is a parameter. In this framework we demonstrate that this model can be used to explain the dark energy dominated universe, and different proper choices of the parameters may lead to three kinds of fates of the cosmological evolution: no future singularity, big rip, or Type-III singularity as presented in [S. Nojiri, S.D. Odintsov, and S. Tsujikawa, Phys. Rev. D 71 (2005) 063004].