Model-independent H0 from GWTC-4 standard sirens and TDCOSMO 2025 strong lensing time delays

Abstract

The significant discrepancy between early- and late-Universe measurements of the Hubble constant, known as the Hubble tension, remains one of the most pressing open questions in cosmology. Since both sides of the tension rely on model-dependent assumptions or multi-rung calibration chains, a cosmological-model-independent measurement of $H_0$ is essential to arbitrate this discrepancy. In this work, we combine 142 gravitational-wave standard siren events from the Fourth Gravitational-Wave Transient Catalog with the latest TDCOSMO2025 time-delay strong lensing data to constrain $H_0$ in a cosmological-model-independent framework based on the distance sum rule. Under the FullPop-4.0 population model with the TDCOSMO2025-only lensing configuration, we obtain $H_0 = 83.78^{+12.53}_{-10.23}\ {\rm km\,s^{-1}\,Mpc^{-1}}$, with a relative precision of $13.58\%$. We find that the $H_0$ precision is governed primarily by the mass-sheet transformation treatment on the strong-lensing side: replacing the conservative TDCOSMO2025 hierarchical framework with the H0LiCOW method tightens the constraint to $H_0 = 75.42^{+3.74}_{-4.66}\ {\rm km\,s^{-1}\,Mpc^{-1}}$, with a relative precision of $5.57\%$. At the current precision, all results are consistent with both the Planck and SH0ES values, and future improvements from more high-redshift dark siren events and more time-delay lens systems are expected to strengthen this model-independent approach.