Gravitational Action Versus Entropy on Simplicial Lattices in Four Dimensions

TL;DR

This paper explores quantum gravity on 4D simplicial lattices using Regge calculus, focusing on the unbounded action problem and the influence of entropy, with numerical evidence for an entropy-dominated region.

Contribution

It provides new numerical evidence for the existence of an entropy-dominated phase in quantum gravity on simplicial lattices, even with unbounded actions.

Findings

Evidence for an entropy-dominated region with well-defined expectation values

Numerical results support the role of entropy in stabilizing the path integral

Analysis includes both regular and irregular triangulations

Abstract

We investigate quantum gravity on simplicial lattices using Regge calculus with special emphasize on the problem of the unbounded action. The role of the entropy for the path integral is discussed in detail. Our numerical results show further evidence for the existence of an entropy dominated region with well defined expectation values even for unbounded action. Analyses are performed both for the standard regular triangulation of the 4-torus and for irregularly triangulated lattices obtained by insertion of vertices using barycentric subdivision.