Clocks and trajectories in quantum cosmology

TL;DR

This paper explores a quantum cosmological model of an empty Bianchi I universe, using a deparametrized Hamiltonian to define a natural clock and examining bouncing trajectories and their symmetry properties.

Contribution

It introduces a novel approach to quantum cosmology by deparametrizing the Hamiltonian and analyzing bouncing trajectories with respect to a shear-based clock.

Findings

Multiple bouncing trajectories identified in the quantum model

Explicit dependence of trajectories on the chosen clock

Analysis of symmetry across the bounce in quantum cosmology

Abstract

We consider a simple cosmological model consisting of an empty Bianchi I Universe, whose Hamiltonian we deparametrise to provide a natural clock variable. The model thus effectively describes an isotropic universe with an induced clock given by the shear. Quantising this model, we obtain various different possible bouncing trajectories (semiquantum expectation values on coherent states or obtained by the de Broglie-Bohm formulation) and explicit their clock dependence, specifically emphasising the question of symmetry across the bounce.