The approximate solution, given by Eq. (28), results in negative q at small t , referring to expansion era. q from the particular solution, Eq. (34) is negative everywhere. For the particular solution, only the scale factor depends on t , Eq. (30). The results are given in the right panel of Fig. 1. All cosmological and thermodynamical quantities given by Eq. (29) and Eqs. (31)-(34) are constant in time. It is obvious that the bulk viscosity plays an important role in the evolution of the Early Universe. Despite of the simplicity of our model, it shows that a better understanding of the dynamics of our Universe is only accessible, if we use reliable equation of state to characterize the matter filling out the cosmic background. We conclude that the causal bulk viscous Universe described by the approximate solution starts its evolution from an initial non-singular state with a non-zero initial value of Hubble parameter H ( t ) and scale factor a ( t ), where t is the comoving time. In this treatment, t is given in GeV − $^{1}$. Also the thermodynamical quantities, energy density ρ for instance, are finite at vanishing t . Even the temperature T itself shows no singularity at t = 0. The Hubble parameter H decreases monotonically with T similar to ρ . The bulk viscous pressure Π likely satisfies the condition that Π < 0 at very small t indicating to inflationary era. Then Π switches to positive value. It reaches a maximum value and then decays and vanishes, exponentially, 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. (28). 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 13 VII. CONCLUSIONS