The Well-Defined Phase of Simplicial Quantum Gravity in Four Dimensions

TL;DR

This paper investigates a stable, well-defined phase of four-dimensional simplicial quantum gravity using the Regge approach, revealing finite observables despite an unbounded action and comparing results with dynamical triangulation methods.

Contribution

It demonstrates the existence of a stable, entropy-dominated phase with finite expectation values in 4D simplicial quantum gravity and compares it with dynamical triangulation results.

Findings

Existence of a stable phase with small negative curvature.

Finite expectation values despite unbounded Einstein-Hilbert action.

Qualitative agreement with dynamical triangulation results.

Abstract

We analyze simplicial quantum gravity in four dimensions using the Regge approach. The existence of an entropy dominated phase with small negative curvature is investigated in detail. It turns out that observables of the system possess finite expectation values although the Einstein-Hilbert action is unbounded. This well-defined phase is found to be stable for a one-parameter family of measures. A preliminary study indicates that the influence of the lattice size on the average curvature is small. We compare our results with those obtained by dynamical triangulation and find qualitative correspondence.