Eq. (\[htideal1\]). The viscous fluid results in finite $H$ even at vanishing $t$, as can be seen from Eq. (\[eq:mysolut1\]).

The scale factor $a(t)$ also shows differences in both cases. $a(t)$ in a Universe with an ideal and non-viscous background matter depends on $t$ according to Eq. (\[atideal1\]), which simply implies that $a(t)$ is directly proportional to $t$, and $a(t)$ vanishes at $t=0$, which shows the existence of a singularity of $H$. Assuming that the background matter is described by a viscous fluid results in different $a(t)$-behaviors with increasing $t$. At $t=0$, $a(t)$ remains finite. Correspondingly, $H(t)$ remains also finite. In general, the dependence on $t$ is much more complicated than in Eq. (\[atideal1\]). Here we have an $A/{\cal P}$ root of an exponential function. If $\exp(-Bt/{\cal P})>>A$, $a$ remains constant.

Fig. \[Figg2\] illustrates the dependence of the two thermodynamical quantities, $\rho $ and $T$, on the comoving time. The non-viscous Universe shows a singular behavior in $\rho$ at vanishing $t$, as shown in the left panel of Fig. \[Figg2\]. This is not obvious in the case where we have taken into consideration a finite viscosity coefficient, i.e., $\rho$ is finite at $t=0$. In both cases, $\rho$ is decreasing with 