Wheeler-DeWitt quantization and singularities

TL;DR

This paper investigates whether quantum cosmology predicts singularities using a Bohmian approach to Wheeler-DeWitt quantization, finding non-zero probabilities for non-singular universes, contrasting with other quantum interpretations.

Contribution

It introduces a Bohmian framework for Wheeler-DeWitt quantum cosmology and compares its predictions on singularities with other approaches, highlighting the dependence on quantum interpretation.

Findings

Non-zero probability for non-singular trajectories with generic wave functions.

Contrasts with consistent histories approach which always predicts singularity.

Qualitative behavior of trajectories is similar across different Bohmian approaches.

Abstract

We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaitre-Robertson-Walker model and investigate the question whether or not there are singularities, in the sense that the universe reaches zero volume. We find that for generic wave functions (i.e., non-classical wave functions), there is a non-zero probability for a trajectory to be non-singular. This should be contrasted to the consistent histories approach for which it was recently shown by Craig and Singh that there is always a singularity. This result illustrates that the question of singularities depends much on which version of quantum theory one adopts. This was already pointed out by Pinto-Neto et al., albeit with a different Bohmian approach. Our current Bohmian approach agrees with the consistent histories approach by Craig and Singh for single-time histories, unlike the one studied earlier by Pinto-Neto et al. Although the trajectories are usually different in the two Bohmian approach, their qualitative behavior is the same for generic wave functions.