Stability Issues in Euclidean Quantum Gravity

TL;DR

This paper discusses the stability challenges in Euclidean quantum gravity, focusing on the unbounded action and the role of zero modes, with insights from numerical simulations and open issues in the field.

Contribution

It analyzes the stability issues related to zero modes in Euclidean quantum gravity and clarifies their non-perturbative implications.

Findings

Perturbation theory about flat space remains effective despite unbounded action.

Numerical simulations provide insights into the non-perturbative behavior.

Zero modes with vanishing integrated scalar curvature are key to understanding stability.

Abstract

It is known that the action of Euclidean Einstein gravity is not bounded from below and that the metric of flat space does not correspond to a minimum of the action. Nevertheless, perturbation theory about flat space works well. The deep dynamical reasons for this reside in the non perturbative behaviour of the system and have been clarified in part by numerical simulations. Several open issues remain. We treat in particular those zero modes of the action for which R(x) is not identically zero, but the integral of sqrt{g(x)} R(x) vanishes.