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 Formula: see text is associated with the fluid as a whole, and (ii) a two-component model where Formula: see text is associated with a dark matter component Formula: see text only, the dark energy component considered inviscid. Shear viscosity is omitted. We assume throughout the simple equation-of-state Formula: see text with Formula: see text a constant. In the one-component model, we consider two possibilities, either to take Formula: see text 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 Formula: see text and the magnitude of Formula: see text, or we consider the case Formula: see text, 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 Formula: see text is proportional to the square of Formula: see text, 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 Formula: see text for the present viscosity is reasonable, and that the two-component model seems to be favored.