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Consistent probabilities in perfect fluid quantum universes
Phys. Rev. D 89, 023514 – Published 21 January, 2014
DOI: https://doi.org/10.1103/PhysRevD.89.023514
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 a possible singular behavior of quantum cosmological models in which the matter content is described by a hydrodynamical perfect fluid, where the resulting wave equation is a genuine Schrödinger 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.
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