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

TL;DR

This paper develops a formalism for bulk viscous solutions in the cosmic fluid, estimates current viscosity limits from observations, and explores implications for the universe's future evolution, including potential big rip scenarios.

Contribution

It introduces a general formalism for bulk viscous solutions in the Friedmann universe and applies it to estimate cosmic viscosity and analyze future cosmological outcomes.

Findings

Current bulk viscosity is estimated to be around 10^6 Pa s.

Observations constrain the magnitude of present-day bulk viscosity.

A specific viscosity-density relation suggests a possible big rip in the future.

Abstract

We derive a general formalism for bulk viscous solutions of the energy-conservation-equation for $\rho(a,\zeta)$, 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 $\zeta_0\sim 10^6~$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 $\zeta$ to analyse the fate of the future universe. Of special interest is the case $\zeta \propto \sqrt{\rho}$ 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.