General Bulk-Viscous Solutions and Estimates of Bulk Viscosity in the Cosmic Fluid

Abstract

We derive a general formalism for bulk viscous solutions of the energy-conservation-equation for $ρ(a,ζ)$, both for a single-component and a multicomponent fluid in the Friedmann universe. For our purposes these general solutions become valuable in estimating order of magnitude of the phenomenological viscosity in the cosmic fluid at present. $H(z)$ observations are found to put an upper limit on the magnitude of the modulus of the present day bulk viscosity. It is found to be $ζ_0\sim 10^6~$Pa s, in agreement with previous works. We point out that this magnitude is acceptable from a hydrodynamic point of view. Finally, we bring new insight by using our estimates of $ζ$ to analyse the fate of the future universe. Of special interest is the case $ζ\propto \sqrtρ$ for which the fluid, originally situated in the quintessence region, may slide through the phantom barrier and inevitably be driven into a big rip. Typical rip times are found to be a few hundred Gy.

15 pages, one figure. Major revision of the manuscript; new title. Version to appear in Entropy