Evolution of the scale factor with the time in linear scales. The dashed line corresponds to the standard radiation model of Section 3.2 exhibiting a finite time singularity at (Big Bang). When quantum mechanics is taken into account (as in our simple semiclassical model), the initial singularity is smoothed-out and the scale factor at is equal to the Planck length . This is similar to a second order phase transition where the Planck constant plays the role of finite size effects (see Section 3.6 for a development of this analogy).