On the Growth of the Number of Hyperbolic Gravitational Instantons with respect to Volume

TL;DR

This paper demonstrates that the count of hyperbolic gravitational instantons increases superexponentially with volume and reveals implications for the Hartle-Hawking wave function, indicating an infinite peak at a specific hyperbolic 3-manifold.

Contribution

It establishes the superexponential growth rate of hyperbolic gravitational instantons and links this to the behavior of the Hartle-Hawking wave function.

Findings

Number of hyperbolic gravitational instantons grows superexponentially with volume

The Hartle-Hawking wave function is infinitely peaked at a certain hyperbolic 3-manifold

Provides a new understanding of quantum cosmology in hyperbolic geometries

Abstract

In this paper, we show that the number of hyperbolic gravitational instantons grows superexponentially with respect to volume. As an application, we show that the Hartle-Hawking wave function for the universe is infinitely peaked at a certain closed hyperbolic 3-manifold.