Characteristic Properties of Two Different Viscous Cosmology Models for the Future Universe

We analyze characteristic properties of two different cosmological models: (i) a one-component dark energy model where the bulk viscosity $\zeta$ is associated with the fluid as a whole, and (ii) a two-component model where $\zeta$ is associated with a dark matter component ${\rho }_{\mathrm{m}}$ only, the dark energy component considered inviscid. Shear viscosity is omitted. We assume throughout the simple equation of state $p=w\rho$, with $w$ a constant. In the one-component model we consider two possibilities, either to take $\zeta$ proportional to the scalar expansion (equivalent to the Hubble parameter), in which case the evolution becomes critically dependent on the value of the small constant $\alpha =1+w$ and the magnitude of $\zeta$. Second, we consider the case $\zeta =$const., where a de Sitter final stage is reached in the future. In the two-component model we consider only the case where the dark matter viscosity ${\zeta }_{\mathrm{m}}$ is proportional to the square of ${\rho }_{\mathrm{m}}$, where again a de Sitter form is found in the future. In this latter case the formalism is supplemented by a phase space analysis. As a general result of our considerations we suggest that a value $\zeta_0\sim 10^6~$Pa s for the present viscosity is reasonable, and that the two-component model seems to be favored.