On the equation of state of a flat FRW model filled with a bulk viscous fluid

TL;DR

This paper investigates the equation of state for a flat FRW cosmological model with bulk viscous fluid, revealing scale invariance only when the viscous parameter is 1/2 and establishing a proportional relationship between viscous pressure and energy density.

Contribution

It demonstrates that the flat FRW model with bulk viscosity admits scaling symmetry only at a specific viscous parameter value and characterizes the equation of state under this condition.

Findings

Scaling symmetry exists iff the viscous parameter γ=1/2.

Bulk viscous pressure is proportional to energy density, Π=κρ, with κ negative.

The model's scale invariance is confirmed under the proportionality assumption.

Abstract

In this paper, we study the equation of state admissible for a flat FRW models filled with a bulk viscous fluid by using the Lie group method. It is founded that the model admits scaling symmetries iff the bulk viscous parameter $\gamma =1/2$. In this case, it is found that the main quantities follow a power law solution and in particular the bulk viscous pressure $\Pi $ has the same order of magnitude as the energy density $\rho ,$ in such a way that it is possible to formulate the equation of state $\Pi =\varkappa \rho ,$ where $\varkappa \in \mathbb{R}^{-}$ (i.e. is a negative numerical constant)$.$ If we assume such relationship we find again that the model is scale invariant iff $\gamma =1/2.$ We conclude that the model accepts a scaling symmetry iff $\gamma =1/2$ and that for this value of the viscous parameter, $\Pi =\varkappa \rho ,$ but the hypothesis $\Pi =\varkappa \rho $ does not imply $\gamma =1/2,$ and that the model is scale invariant.