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

TL;DR

This paper compares two viscous cosmology models, analyzing their future evolution and suggesting the two-component model with dark matter viscosity is more consistent, with implications for understanding the universe's fate.

Contribution

It introduces and compares two different viscous cosmological models, providing phase space analysis and suggesting the two-component model is more favored.

Findings

De Sitter future stage in both models.

Two-component model with dark matter viscosity is preferred.

Estimated present viscosity value around 10^6 Pa s.

Abstract

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 $\rho_{\rm m}$ 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 $\zeta_{\rm m}$ is proportional to the square of $\rho_{\rm m}$, 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.