Scaling Exponents for Lattice Quantum Gravity in Four Dimensions

© 2015 American Physical Society. 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 ν=1/3. The lattice results are generally consistent with gravitational antiscreening, which would imply a slow increase in the strength of the gravitational coupling with distance, and presented herein are detailed estimates for exponents and amplitudes characterizing this slow rise. 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 λ, which in gravity acts as an effective nonperturbative infrared cutoff. In this nonperturbative vacuum condensate picture a fundamental relationship emerges among 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 slow infrared growth of G with distance should become observable only on very large distance scales, comparable to λ. One may hope that future high precision satellite experiments could possibly come within reach of this small quantum correction, as suggested by the vacuum condensate picture of quantum gravity.