A new study has employed a combination of gravitational wave standard sirens and time-delay gravitational lensing data to obtain a measurement of the Hubble parameter, H0, independent of the cosmological model. The goal is to address the persistent Hubble tension, a significant discrepancy between H0 measurements in the early universe (such as those from Planck) and in the late universe (such as those from the SH0ES project). Since both approaches rely on model-dependent assumptions or multi-step calibration chains, a determination of H0 that does not depend on a specific cosmological model is crucial for resolving this divergence.

The researchers combined 142 gravitational wave standard siren events from the Fourth Gravitational-Wave Transient Catalog (GWTC-4) with the latest time-delay strong gravitational lensing data from TDCOSMO2025. Using a cosmological model-independent framework based on the distance sum rule, they obtained a value of H0 = 83.78 +12.53 -10.23 km s -1 Mpc -1, with a relative precision of 13.58%. This measurement was obtained under the FullPop-4.0 population model and the TDCOSMO2025-only lensing configuration.

The study also reveals that the precision of H0 is strongly influenced by the treatment of the mass sheet transformation on the strong lensing side. By replacing the conservative hierarchical framework of TDCOSMO2025 with the H0LiCOW method, the constraint was tightened to H0 = 75.42 +3.74 -4.66 km s -1 Mpc -1, with a relative precision of 5.57%. At current precision, all results are consistent with both Planck and SH0ES values. Future improvements, such as more high-redshift dark siren events and a larger number of time-delay lensing systems, are expected to further strengthen this model-independent approach.