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A null test of the Hubble tension

Gerasimos Kouniatalis, Emmanuel N. Saridakis

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.

A null test of the Hubble tension

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 , 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.
Paper Structure (8 sections, 11 equations, 1 figure)

This paper contains 8 sections, 11 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Geometric construction
  3. The null test and its interpretation
  4. Discussion and conclusions

Figures (1)

  • Figure 1: Schematic overview of the proposed $H_0$-independent consistency test. (a) Geometry of a strongly lensed gravitational-wave event: a lens at redshift $z_{\rm d}$ produces multiple images of a source at $z_{\rm s}$. The measured time delays determine the time-delay distance $D_{\Delta t}(z_{\rm d},z_{\rm s})$, while the gravitational-wave amplitude yields the luminosity distance $D_L(z_{\rm s})$. (b) Conceptual structure of the null test: the observed ratio $R_{\rm obs}=D_{\Delta t}/D_L$, in which the overall normalization of the expansion rate is eliminated, is directly compared with the corresponding early-Universe prediction $R_{\rm CMB}(z_{\rm d},z_{\rm s})$.