Consistent Probabilities in Perfect Fluid Quantum Universes

TL;DR

This paper investigates Wheeler-DeWitt quantum cosmology with perfect fluid matter, showing that in certain models, different quantum interpretations agree on singularity avoidance, but face issues with positive curvature.

Contribution

It demonstrates the equivalence of Consistent Histories and de Broglie-Bohm approaches in perfect fluid models where singularities are avoided.

Findings

Singularities are eliminated in models with non-positive spatial curvature.

Consistent Histories and de Broglie-Bohm approaches agree in these models.

Positive curvature models lack a consistent history framework.

Abstract

Recently it has been claimed that the Wheeler-DeWitt quantization of gravity is unable to avoid cosmological singularities. However, in order to make this assertion, one must specify the underlying interpretation of quantum mechanics which has been adopted. For instance, several nonsingular models were obtained in Wheeler-DeWitt quantum cosmology in the framework of the de Broglie-Bohm quantum theory. Conversely, there are specific situations where the singularity cannot be avoided in the framework of the Consistent Histories approach to quantum mechanics. In these specific situations, the matter content is described by a scalar field, and the Wheeler-DeWitt equation looks-like a Klein-Gordon equation. The aim of this work is to study the Wheeler-DeWitt quantization of cosmological models where the matter content is described by an hydrodynamical perfect fluid, where the Wheeler-DeWitt equation reduces to a genuine Schr\"odinger equation. In this case, it is shown that the conclusions of the Consistent Histories and the de Broglie-Bohm approaches coincide in the quantum cosmological models where the curvature of the spatial sections is not positive definite, namely, that the cosmological singularities are eliminated. In the case of positive spatial curvature, the family of histories is no longer consistent, and no conclusion can be given in this framework.