A Note on Real Tunneling Geometries

TL;DR

This paper completes a proof showing that in three-dimensional quantum cosmology, real tunneling geometries are probable, meaning they significantly contribute as maxima in the semiclassical wave function, supporting the Hartle-Hawking no boundary proposal.

Contribution

It extends previous work by proving the likelihood of real tunneling geometries in three-dimensional models within quantum cosmology.

Findings

Real tunneling geometries are probable in 3D quantum cosmology.

Such geometries correspond to maxima of the semiclassical wave function.

Supports the Hartle-Hawking no boundary proposal.

Abstract

In the Hartle-Hawking ``no boundary'' approach to quantum cosmology, a real tunneling geometry is a configuration that represents a transition from a compact Riemannian spacetime to a Lorentzian universe. I complete an earlier proof that in three spacetime dimensions, such a transition is ``probable,'' in the sense that the required Riemannian geometry yields a genuine maximum of the semiclassical wave function.