Peaks in the Hartle-Hawking Wave Function from Sums over Topologies

TL;DR

This paper demonstrates that in quantum cosmology with negative cosmological constant, the Hartle-Hawking wave function exhibits sharp peaks at specific geometries, indicating a potential mechanism for local homogeneity.

Contribution

It introduces a novel approach using Einstein Dehn filling to identify peaks in the Hartle-Hawking wave function related to topologically close Einstein manifolds.

Findings

Wave function peaks at constant negative curvature metrics

Peaks are calculable and tied to topological features

Suggests a new mechanism for local homogeneity in quantum cosmology

Abstract

Recent developments in ``Einstein Dehn filling'' allow the construction of infinitely many Einstein manifolds that have different topologies but are geometrically close to each other. Using these results, we show that for many spatial topologies, the Hartle-Hawking wave function for a spacetime with a negative cosmological constant develops sharp peaks at certain calculable geometries. The peaks we find are all centered on spatial metrics of constant negative curvature, suggesting a new mechanism for obtaining local homogeneity in quantum cosmology.