Wheeler-DeWitt quantization and singularities

We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaitre-Robertson-Walker model and investigate the question of whether or not there are singularities, in the sense that the Universe reaches zero volume. We find that for generic wave functions (i.e., nonclassical wave functions), there is a nonzero probability for a trajectory to be nonsingular. 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 approaches, their qualitative behavior is the same for generic wave functions.