$, $\xi\sim  \alpha_s^2 T^3/\ln \alpha_s^{-1}$ and $\eta\sim T^3/(\alpha_s^2 \ln
\alpha_s^{-1})$ [@mueller3]. 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 $(\epsilon-3p)/T^4$  [@karsh09], where $\epsilon$ and $p$ are energy and pressure density, respectively. In the quenched lattice QCD, the ratio $\zeta/s$ seems to diverge near $T_c$ [@meyer08].

To avoid the mathematical difficulties accompanied with the Abel second type non-homogeneous and non-linear differential equations [@TawCosmos], one used to model the cosmological fluid as an ideal (non-viscous) fluid. No doubt that the viscous treatment of the cosmological background should have many essential consequences [@taw08]. The thermodynamical ones, for instance, can profoundly modify the dynamics and configurations of the whole cosmological background [@conseq1]. The reason is obvious. The bulk viscosity is to be expressed as a function of the Universe energy density $\rho$ [@conseq2]. Much progress has been achieved in relativistic thermodynamics of dissipative fluids. The pioneering theories of Eckart [@Ec40] and Landau and Lifshitz [@LaLi87] suffer from lake of causality constrains. The currently used theory is the Israel and Stewart theory [@Is76; @IsSt76], in which the causality is conserved and 