at large $t$. The deceleration parameter $q$ shows an expanding behavior in the case of non-viscous ideal gas and first particular solution. For second particular solution, $q$ starts from zero and increases, exponentially. According to this solution, the Universe was decelerating. The approximate solution shows an interesting behavior in $q(t)$, Eq. (\[approx-q\]). At small $t$, the values of $q$ are negative, i.e. the Universe was accelerating (expansion). At larger $t$, a non-inflationary behavior sets on, $q>0$, i.e., the Universe switched to a decelerating evolution.

In this treatment, we assumed that the Universe is flat, $k=0$, and the background geometry is filled out with QCD matter (QGP) with a finite viscosity coefficient. The resulting Universe is obviously characterized by a shortly increasing and afterward constant scale factor and a fast vanishing Hubble parameter. At $t=0$, both $a(t)$ and $H(t)$ remain finite, i.e., there is no singularity. The validity of our treatment depends on the validity of the equations of states, Eq. \[13\], which we have deduced from the lattice QCD simulations at temperatures larger than $T_c\approx 0.19~$GeV. Below $T_c$, as the Universe cooled down, not only the degrees of freedom suddenly increase [@Tawfik03] but also the equations of state turn to 