New Developments in the Spectral Asymptotics of Quantum Gravity

TL;DR

This paper investigates the spectral properties of quantum gravity on a Euclidean 4-ball, revealing a vanishing one-loop wave function that hints at quantum avoidance of the cosmological singularity due to spectral cancellations.

Contribution

It introduces a novel spectral cancellation mechanism in quantum gravity on a Euclidean 4-ball under diffeomorphism-invariant boundary conditions, impacting the understanding of quantum cosmology.

Findings

Vanishing one-loop wave function in the small three-geometry limit

Spectral cancellation on the Euclidean 4-ball

Implication of quantum avoidance of the cosmological singularity

Abstract

A vanishing one-loop wave function of the Universe in the limit of small three-geometry is found, on imposing diffeomorphism-invariant boundary conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory. All of this is made possible by a peculiar spectral cancellation on the Euclidean 4-ball, here derived and discussed.