Light ray fluctuation and lattice refinement of simplicial quantum gravity

TL;DR

This paper investigates how lattice refinement in Lorentzian simplicial quantum gravity affects light ray fluctuations in 3D and 4D, revealing a potential fixed point and the transition from wild microscopic to mild macroscopic fluctuations.

Contribution

It provides the first numerical analysis of light ray fluctuations across different lattice refinements in Lorentzian simplicial quantum gravity, suggesting a fixed point and universality class.

Findings

Lattice refinement does not simply suppress or enhance fluctuations.

Fluctuations tend towards intermediate distributions with refinement.

Hints of a lattice refinement fixed point related to universality classes.

Abstract

In several approaches of non-perturbative quantum gravity, a major outstanding problem is to obtain results valid at the infinite lattice refinement limit. Working with Lorentzian simplicial quantum gravity, we compute light ray fluctuation probabilities in 3D and 4D across different lattices. In a simplified refined box model with the Einstein-Hilbert action, numerical results show that lattice refinement does not simply suppress or simply enhance light ray fluctuations, but actually drives very wide and very narrow light probability distributions towards intermediate ones. A comparison across lattices and across couplings reveals numerical hints at a lattice refinement fixed point associated with a universality class of couplings. The results fit the intuition that quantum spacetime fluctuations reflected by light ray fluctuations start wild microscopically and become mild macroscopically. The refined box model is limited by the assumption of a rigid frame at all scales. The present results suggest further studies around the zero-coupling limit to relax the simplifying assumptions of the model.