Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I

TL;DR

This paper investigates how to define physical evolution in vacuum Bianchi I Loop Quantum Cosmology without a scalar field clock, using partial observables related to geometric variables, and confirms the robustness of quantum bounces.

Contribution

It introduces new methods to describe evolution in LQC without matter fields, using geometric variables as parameters, and analyzes their applicability and physical interpretation.

Findings

Physical evolution can be described using geometric variables as parameters.

The quantum bounce remains robust even without matter fields.

Semiclassicality is preserved through the bounce.

Abstract

We use the vacuum Bianchi I model as an example to investigate the concept of physical evolution in Loop Quantum Cosmology (LQC) in the absence of the massless scalar field which has been used so far in the literature as an internal time. In order to retrieve the system dynamics when no such a suitable clock field is present, we explore different constructions of families of unitarily related partial observables. These observables are parameterized, respectively, by: (i) one of the components of the densitized triad, and (ii) its conjugate momentum; each of them playing the role of an evolution parameter. Exploiting the properties of the considered example, we investigate in detail the domains of applicability of each construction. In both cases the observables possess a neat physical interpretation only in an approximate sense. However, whereas in case (i) such interpretation is reasonably accurate only for a portion of the evolution of the universe, in case (ii) it remains so during all the evolution (at least in the physically interesting cases). The constructed families of observables are next used to describe the evolution of the Bianchi I universe. The performed analysis confirms the robustness of the bounces, also in absence of matter fields, as well as the preservation of the semiclassicality through them. The concept of evolution studied here and the presented construction of observables are applicable to a wide class of models in LQC, including quantizations of the Bianchi I model obtained with other prescriptions for the improved dynamics.