or small perturbations around it [12]. The Einstein field equations for homogeneous models with dissipative fluids can be decoupled and therefore are reduced to an autonomous system of first order ordinary differential equations, which can be analyzed qualitatively [13]. The role of a transient bulk viscosity in a FRW space-time with decaying vacuum has been discussed in [14]. Models with causal bulk viscous cosmological fluid have been considered recently [15]. They obtained both power-law and inflationary solutions, with the gravita- tional constant an increasing function of time. The dynamics of a viscous cosmological fluids in the generalized Randall-Sundrum model for an isotropic brane were considered in [16]. The renormalization group method was applied to the study of homogeneous and flat FRW Universes, filled with a causal bulk viscous cosmological fluid, in [17]. A generalization of the Chaplygin gas model, by assuming the presence of a bulk viscous type dissipative term in the effective thermodynamic pressure of the gas, was investigated recently in [18]. Recent RHIC results give a strong indication that in the heavy-ion collisions experiments, a hot dense matter can be formed [19]. Such an experimental evidence might agree with the ”new state of matter” as predicted in the Lattice QCD simulations [20]. However, the experimentally observed elliptic flow in peripheral heavy-ion collisions seems to indicate that a thermalized collective QCD matter has been produced. In a addition to that, the success of ideal fluid dynamics in explaining several experimental data e.g. transverse momentum spectra of identified particles, elliptic flow [21], together with the string theory motivated that the shear viscosity η to the entropy s would have the lower limit ≈ 1 / 4 π [22] leading to a paradigm that in heavy- ion collisions, that a nearly perfect fluid likely be created and the quarks and gluons likely go through relatively rapid equilibrium characterized with a thermalization time less than 1 fm/c [23]. According to recent lattice QCD simulations [24], the bulk viscosity ξ is not negligible near the QCD critical temperature T$_{c}$ . It has been shown that the bulk and shear viscosity at high temperature T and weak coupling α$_{s}$ , ξ ∼ α 2 $_{s}$T $^{3}$/ ln α − 1 s and η ∼ T $^{3}$/ ( α 2 s ln α − 1 s ) [26]. Such a behavior obviously reflects the fact that near T$_{c}$ QCD is far from being conformal. But at high T , QCD approaches conformal invariance, which can be indicated by low trace anomaly ( ϵ − 3 p ) /T 4 [27], where ϵ and p are energy and pressure density, respectively. In the quenched lattice QCD, the ratio ζ/s seems to diverge near T$_{c}$ [28]. To avoid the mathematical difficulties accompanied with the Abel second type non- homogeneous and non-linear differential equations [29], one used to model the cosmological 3