A null test of the Hubble tension

TL;DR

This paper introduces a new geometric null test combining gravitational lensing and gravitational waves to independently assess the origin of the Hubble tension, distinguishing between early and late Universe explanations.

Contribution

It proposes a Hubble-constant-independent ratio from lensing and gravitational-wave data to test the expansion history and the origin of the Hubble tension.

Findings

The ratio depends only on redshift and expansion rate.

It can be predicted from early-Universe data.

It can be measured directly at late times.

Abstract

The origin of the Hubble tension remains one of the central open problems in modern cosmology, with competing explanations invoking either early-Universe physics, late-time modifications of cosmic expansion, or unresolved observational systematics. In this Letter we propose a new, purely geometric null test of the late-time expansion history that is exactly independent of the Hubble constant. By combining strong-lensing time-delay distances with gravitational-wave standard-siren luminosity distances, we construct a dimensionless ratio that depends only on the redshift dependence of the expansion rate and can be both predicted from early-Universe data and measured directly at late times, without relying on the cosmic distance ladder or the sound horizon. We show that the comparison between the early- and late-time determinations of this ratio provides a transparent consistency test of the standard cosmological expansion. When combined with an independent standard-siren measurement of $H_{0}$, this framework allows one to unambiguously distinguish between early- and late-time origins of the Hubble tension. With the forthcoming detection of lensed gravitational-wave standard sirens, the proposed test provides a timely and robust framework for probing this long-standing cosmological puzzle.