Pregeometry and euclidean quantum gravity

TL;DR

This paper proposes a formulation of euclidean pregeometry as an SO(4) Yang-Mills theory with additional fields, leading to a well-behaved quantum gravity model that reproduces general relativity at large scales.

Contribution

It introduces a novel pregeometric framework for euclidean quantum gravity using gauge fields and a vector field, ensuring a well-defined functional integral and ghost-free propagators.

Findings

Propagators are well-behaved at short distances.

The model reproduces general relativity at large scales.

Graviton propagator is free of ghost or tachyonic poles.

Abstract

Einstein's general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a $SO(4)$ - Yang-Mills theory. In addition to the gauge fields we include a vector field in the vector representation of the gauge group. The gauge - and diffeomorphism - invariant kinetic terms for these fields permit a well-defined euclidean functional integral, in contrast to metric gravity with the Einstein-Hilbert action. The propagators of all fields are well behaved at short distances, without tachyonic or ghost modes. The long distance behavior is governed by the composite metric and corresponds to general relativity. In particular, the graviton propagator is free of ghost or tachyonic poles despite the presence of higher order terms in a momentum expansion of the inverse propagator. This pregeometry seems to be a valid candidate for euclidean quantum gravity, without obstructions for analytic continuation to a Minkowski signature of the metric.