Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-12-19
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages, Revtex4
Scientific paper
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.
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