Polymer dynamics of isotropic universe in Ashtekar and in volume variables

TL;DR

This paper investigates the polymer quantum dynamics of the isotropic universe using Ashtekar variables and volume variables, revealing differences in the nature of the Big Bounce and implications for Loop Quantum Cosmology schemes.

Contribution

It compares polymer dynamics in different variable representations and discusses the implications for the nature of the Big Bounce and the viability of LQC schemes.

Findings

The volume variable yields a universal bounce cutoff.

The connection variable fixes the bounce energy density by initial conditions.

Comparison with Loop Quantum Cosmology highlights differences in bounce nature.

Abstract

We analyze the semiclassical and quantum polymer dynamics of the isotropic Universe in terms of both the standard Ashtekar-Barbero-Immirzi connection and its conjugate momentum and also of the new generalized coordinate conjugate to the Universe volume. We study the properties 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 Bounce energy density is fixed by the initial conditions on the prepared wavepacket. As a phenomenological implication, we introduce particle creation as a dissipative term and study the production of entropy in the two formulations. Then, we compare the obtained dynamics 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 privileged character of the Ashtekar-Barbero-Immirzi connection suggests that the natural scenario in the polymer framework is a Big Bounce that is not a Universal cut-off. However, by a parallelism between the polymer and Loop Quantum Cosmology properties of the basic operators, we also develop some considerations in favour of the viability of the $\bar{\mu}$ scheme of Loop Quantum Cosmology on a semiclassical level.