Scaling Exponents for Lattice Quantum Gravity in Four Dimensions

TL;DR

This paper investigates nonperturbative quantum gravity using lattice methods, presenting new results on critical exponents and amplitudes, and supporting the idea of gravitational anti-screening with slow coupling growth at large distances.

Contribution

It provides the first detailed lattice estimates of critical exponents and amplitudes in four-dimensional quantum gravity, linking these to the cosmological constant and infrared behavior.

Findings

Lattice results are consistent with gravitational anti-screening.

The quantum theory depends on a small set of physical parameters.

The growth of G with distance is linked to the cosmological constant.

Abstract

In this work nonperturbative aspects of quantum gravity are investigated using the lattice formulation, and some new results are presented for critical exponents, amplitudes and invariant correlation functions. Values for the universal scaling dimensions are compared with other nonperturbative approaches to gravity in four dimensions, and specifically to the conjectured value for the universal critical exponent $\nu =1 /3$. It is found that the lattice results are generally consistent with gravitational anti-screening, which would imply a slow increase in the strength of the gravitational coupling with distance, and here detailed estimates for exponents and amplitudes characterizing this slow rise are presented. Furthermore, it is shown that in the lattice approach (as for gauge theories) the quantum theory is highly constrained, and eventually by virtue of scaling depends on a rather small set of physical parameters. Arguments are given in support of the statement that the fundamental reference scale for the growth of the gravitational coupling $G$ with distance is represented by the observed scaled cosmological constant $\lambda$, which in gravity acts as an effective nonperturbative infrared cutoff. In the vacuum condensate picture a fundamental relationship emerges between the scale characterizing the running of $G$ at large distances, the macroscopic scale for the curvature as described by the observed cosmological constant, and the behavior of invariant gravitational correlation functions at large distances. Overall, the lattice results suggest that the infrared slow growth of $G$ with distance should become observable only on very large distance scales, comparable to $\lambda$. It is hoped that future high precision satellite experiments will possibly come within reach of this small quantum correction, as suggested by a vacuum condensate picture of quantum gravity.