A note on the vacuum structure to lattice Euclidean quantum gravity

TL;DR

This paper explores the unique vacuum structure of lattice Euclidean quantum gravity, highlighting differences from other quantum field theories and emphasizing the scale-dependent nature of gravitational fluctuations.

Contribution

It provides an analysis of the vacuum structure in lattice Euclidean quantum gravity, revealing significant differences from known vacua in QED and QCD, especially at small scales.

Findings

Long-wavelength vacuum structure resembles QED.

Quantum fluctuations in gravity are reduced compared to QED.

Small-scale fluctuations are comparable to most probable values of geometrical degrees of freedom.

Abstract

It is shown that the ground state or vacuum to the lattice Euclidean quantum gravity is significantly different from the ground states to the well-known vacua in QED, QCD, et cetera. In the case of the lattice Euclidean quantum gravity, the long-wavelength scale vacuum structure is similar to that in QED, moreover the quantum fluctuations to gravity are very reduced in comparison with the situation in QED. But the small scale (of the order of the lattice scale) vacuum structure to gravity is significantly different from that to the long-wavelength scales: the fluctuation values of geometrical degrees of freedom (tetrads) are commensurable with theirs most probable values.