one dot denotes derivative with respect to the time $t$, $G$ is the gravitational constant and $a$ is the scale factor.

Assuming that the total matter content of the Universe is conserved, $T_{i;j}^j=0$, the energy density of the cosmic matter fulfills the conservation law: $$\label{5}
\dot{\rho}+3H\left( p_{eff}+\rho \right) =0,$$ where we introduced the Hubble parameter $H=\dot{a}/a$. In presence of bulk viscous stress $\Pi $, the effective thermodynamic pressure term becomes $p_{eff}=p+\Pi $. Then Eq. (\[5\]) can be written as $$\label{6}
\dot{\rho}+3H\left( p+\rho \right) =-3\Pi H.$$

For the evolution of the bulk viscous pressure we adopt the causal evolution equation [@Ma95], obtained in the simplest way (linear in $\Pi)$ to satisfy the $H$-theorem (i.e., for the entropy production to be non-negative, $S_{;i}^{i}=\Pi^{2}/\xi T\geq0$ [@Is76; @IsSt76]). According to the causal relativistic Israel-Stewart theory, the evolution equation of the bulk viscous pressure reads [@Ma95] $$\label{8}
\tau \dot{\Pi}+\Pi =-3\xi H-\frac{1}{2}\tau \Pi \left( 3H+\frac{\dot{\tau}}{\tau }-\frac{\dot{\xi}}{\xi }-\frac{\dot{T}}{T}\right).$$ In order to have a closed system from equations (\[2\]), (\[6\]) and (\[8\]) we have to add the equations of state for $p$ and $T$.

As shown in Appendix A, the equation of state, the temperature and the bulk viscosity of the quark-gluon plasma (QGP), can be determined approximately 