On the semiclassical and quantum picture of the Bianchi I polymer dynamics

TL;DR

This paper explores the semiclassical and quantum dynamics of Bianchi I cosmology with a scalar field, revealing a universal Big Bounce behavior and analyzing quantum wave packet evolution.

Contribution

It introduces a comprehensive analysis of Bianchi I dynamics using multiple variables and demonstrates the universal nature of the Big Bounce in both semiclassical and quantum frameworks.

Findings

Big Bounce appears in all variable sets in semiclassical analysis.

Polymer-modified Friedmann equation shows a maximum critical density.

Quantum wave packets exhibit features consistent with semiclassical trajectories.

Abstract

We analyze the Bianchi I cosmology in the presence of a massless scalar field and describe its dynamics via a semiclassical and quantum polymer approach. We investigate the morphology of the emerging Big Bounce by adopting three different sets of configurational variables: the natural Ashtekar connections, the Universe volume plus two anisotropy coordinates and a set of anisotropic volume-like coordinates (the latter two sets of variables would coincide in the case of an isotropic Universe). In the semiclassical analysis we demonstrate that the Big Bounce emerges in the dynamics for all the three sets of variables. Moreover, when the Universe volume itself is considered as a configurational variable, we have derived the polymer-modified Friedmann equation and demonstrated that the Big Bounce has a universal nature, i.e. the total critical energy density has a maximum value fixed by fundamental constants and the Immirzi parameter only. From a pure quantum point of view, we investigate the Bianchi I dynamics only in terms of the Ashtekar connections. In particular, we apply the Arnowitt-Deser-Misner (ADM) reduction of the variational principle and then we quantize the system. We study the resulting Schr\"{o}dinger dynamics, stressing that the wave packet peak behavior over time singles out common features with the semiclassical trajectories.