Discrete gravity dynamics from effective spin foams

TL;DR

This paper presents the first numerical computation of spin foam dynamics incorporating an inner edge, testing quantum gravity equations of motion and revealing a complex semiclassical regime influenced by multiple parameters.

Contribution

It introduces an effective spin foam model for dynamics computation, addressing the flatness problem and exploring the semiclassical regime in quantum gravity.

Findings

Rich semiclassical regime identified

Interplay of parameters influences dynamics

Exposes the generic nature of semiclassical behavior in constrained systems

Abstract

The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently introduced effective spin foam models, which are particularly numerically efficient. Previous work has raised the concern of a flatness problem in spin foam dynamics, identifying the potential for the dynamics to lead to flat geometries in the small $\hbar$ semiclassical limit. The numerical results presented here expose a rich semiclassical regime, but one that must be understood as an interplay between the various parameters of the spin foam model. In particular, the scale of the triangulation, fixed by the areas of its boundary triangles, the discreteness of the area spectrum, input from Loop Quantum Gravity, and the curvature scales around the bulk triangles, all enter the characterization of the semiclassical regime identified here. In addition to these results on the dynamics, we show that the subtle nature of the semiclassical regime is a generic feature of the path integral quantization of systems with second class constraints.