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

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 $γ=1/2$. In this case, it is found that the main quantities follow a power law solution and in particular the bulk viscous pressure $Π$ has the same order of magnitude as the energy density $ρ,$ in such a way that it is possible to formulate the equation of state $Π=\varkappa ρ,$ 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 $γ=1/2.$ We conclude that the model accepts a scaling symmetry iff $γ=1/2$ and that for this value of the viscous parameter, $Π=\varkappa ρ,$ but the hypothesis $Π=\varkappa ρ$ does not imply $γ=1/2,$ and that the model is scale invariant.