On the Gravitational Scaling Dimensions

TL;DR

This paper investigates a lattice-based model of quantized gravity, finding a universal critical exponent and proposing a relationship between fundamental gravitational constants, with potential observable implications.

Contribution

It provides a detailed finite size scaling and renormalization group analysis of a simplicial lattice model for quantum gravity, estimating the critical exponent and exploring phenomenological consequences.

Findings

Critical exponent for gravitation $ u=1/3$

Relationship between Newton's constant and curvature

Potential testable phenomenological implications

Abstract

A model for quantized gravitation based on the simplicial lattice discretization is studied in detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are consistent with a value for the universal critical exponent for gravitation $\nu=1/3$, and suggest a simple relationship between Newton's constant, the gravitational correlation length and the observable average space-time curvature. Some perhaps testable phenomenological implications of these results are discussed. To achieve a high numerical accuracy in the evaluation of the lattice path integral a dedicated parallel machine was assembled.