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

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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= ρ, where ∈ 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= ρ, but the hypothesis Π= ρ does not imply γ=1/2, and that the model is scale invariant.