Polymer quantum dynamics of the isotropic Universe by the Ashtekar-Barbero-Immirzi variables: a comparison with LQC.

We analyze the semiclassical and quantum polymer dynamics of the isotropic Universe in terms of both the standard Ashtekar-Barbero-Immirzi connection together with its conjugate momentum and also of the restated connection conjugate to the Universe volume. We study the morphology of the resulting bouncing cosmology that emerges in both the representations and we show that the Big Bounce is an intrinsic cut-off on the cosmological dynamics only when the volume variable is implemented, while in terms of the standard connection the Universe critical density is fixed by the initial conditions on the prepared wavepacket. Then, we compare the obtained results with what emerges in Loop Quantum Cosmology, where the same difference in the nature of the Big Bounce is associated to fixing a minimum area eigenvalue in a comoving or in a physical representation. We conclude that the necessity to account for the zero eigenvalue of the geometrical operators and the privileged character of the Ashtekar-Barbero-Immirzi connection suggest that the most reliable scenario is a Big Bounce whose critical density depends on the Universe initial conditions.