  We analyse the semi-classical and quantum dynamics of the isotropic Universe
in the framework of the Polymer Quantum mechanics, in order to implement a
cut-off physics on the initial singularity. We first identify in the Universe
cubed scale factor (i.e. the spatial volume) the suitable configuration
variable, providing a constant critical energy density, such that the Bounce
arises as intrinsic geometric feature. We then investigate the obtained
semi-classical Bounce dynamics for the primordial Universe, and we outline its
impact on the resolution of cosmological paradoxes, as soon as the
semi-classical evolution is extended (in the spirit of the Ehrenfest theorem)
to the collapsing pre-Bounce Universe. Finally, we validate the use of the
semi-classical effective dynamics by investigating the behaviour of the
expectation values of a proper semiclassical states. The present analysis has
the merit to enforce the equivalence between the Polymer quantization paradigm
in the Minisuperspace and the Loop Quantum Cosmology approach. In fact, our
study allows to define a precise correspondence between the Polymer cut-off
scale and the discrete geometric structure of LQG.
