Topology Change in Canonical Quantum Cosmology

TL;DR

This paper develops a canonical quantum cosmology model allowing topology change in homogeneous hypersurfaces, analyzing solutions of the Wheeler-DeWitt equation and showing that topology change depends on the interpretative framework used.

Contribution

It introduces a midisuperspace quantization framework that permits the study of topology change in quantum cosmology, highlighting interpretative dependence of such phenomena.

Findings

Some solutions exhibit topology change in the hypersurfaces.

Topology change is allowed under the conditional probability interpretation.

Selection rules prevent topology change under the usual probabilistic interpretation.

Abstract

We develop the canonical quantization of a midisuperspace model which contains, as a subspace, a minisuperspace constituted of a Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar and dust fields, where the sign of the intrinsic curvature of the spacelike hypersurfaces of homogeneity is not specified, allowing the study of topology change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the midisuperspace model restricted to this minisuperspace subspace in the semi-classical approximation. Adopting the conditional probability interpretation, we find that some of the solutions present change of topology of the homogeneous hypersurfaces. However, this result depends crucially on the interpretation we adopt: using the usual probabilistic interpretation, we find selection rules which forbid some of these topology changes.