finite, i.e., there is no singularity. The validity of our treatment depends on the validity of the equations of states, Eq. 9, which we have deduced from the lattice QCD simulations at temperatures larger than T$_{c}$ ≈ 0 . 19 GeV. Below T$_{c}$ , as the Universe cooled down, not only the degrees of freedom suddenly increase [36] but also the equations of state turn to be the ones characterizing the hadronic matter. Such a phase transition - from QGP to hadronic matter - would characterize one end of the validity of our treatment. The other limitation is the very high temperatures (energies), at which the strong coupling α$_{s}$ entirely vanishes. 14