Atomic clocks and gravitational waves as probes of non-metricity

TL;DR

This paper explores how atomic clocks and gravitational waves can be used to detect or constrain non-metricity in spacetime, providing new experimental tests for extensions of General Relativity.

Contribution

It formulates gauge-invariant observable effects of non-metricity within Weyl geometry and derives constraints from current atomic-clock and gravitational-wave data.

Findings

Atomic-clock experiments set bounds on non-metricity effects.

Gravitational-wave observations constrain dynamical non-metric degrees of freedom.

Absence of deviations from GR limits non-metricity models.

Abstract

Non-metricity provides a natural extension of Riemannian geometry, yet its experimental signatures remain largely unexplored. In this work we investigate how spacetime non-metricity can be probed through high-precision observations, focusing on atomic clocks and gravitational waves as complementary tools. Working within Weyl geometry as a minimal realization of vectorial non-metricity, we formulate observable effects in a gauge-invariant manner and show that they are associated with path-dependent length transport governed by the Weyl field strength. We derive constraints from atomic-clock experiments and demonstrate that, although gravitational waves do not directly source the Weyl field at linear order, its dynamical contribution induces a backreaction on gravitational-wave propagation, leading to an anomalous strain. As a result, the absence of deviations from General Relativity in current gravitational-wave observations already places meaningful and strong constraints on dynamical non-metric degrees of freedom.