Peaks in the Hartle–Hawking wavefunction from sums over topologies

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 wavefunction for a spacetime with a negative cosmological constant develops sharp peaks at certain calculable geometries. The peaks we find are all centred on spatial metrics of constant negative curvature, suggesting a new mechanism for obtaining local homogeneity in quantum cosmology.