Orbifolds, Quantum Cosmology, and Nontrivial Topology

TL;DR

This paper explores how including nontrivial spatial topologies via orbifolds can extend quantum cosmology models, specifically using 4-orbifolds with singularities to incorporate complex topologies in the universe's quantum creation.

Contribution

It introduces a method to include nontrivial topologies in quantum cosmology by generalizing the sum over manifolds to orbifolds with singularities, focusing on 4-spherical orbifolds.

Findings

Inclusion of orbifolds allows for nontrivial topologies in quantum cosmology.

Analysis of 4-spherical orbifolds with cone-point singularities.

Potential extension of path integral approach to more complex topologies.

Abstract

In order to include nontrivial spatial topologies in the problem of quantum creation of a universe, it seems to be necessary to generalize the sum over compact, smooth 4-manifolds to a sum over finite-volume, compact 4-orbifolds. We consider in detail the case of a 4-spherical orbifold with a cone-point singularity. This allows for the inclusion of a nontrivial topology in the semiclassical path integral approach to quantum cosmology, in the context of a Robertson-Walker minisuperspace.