Cosmology is going through a dramatic moment: the two most precise methods for measuring the expansion rate of the Universe yield incompatible results. On one hand, analysis of the cosmic microwave background by the Planck satellite points to a value around 67 (km/s)/Mpc within the standard cosmological model. On the other, the distance ladder calibrated with Cepheids and supernovae gives about 73. This discrepancy, known as the 'Hubble tension,' has reached the 6σ level and could hint at new physics. The problem is that both approaches depend on chains of assumptions: either about the nature of dark matter and the early Universe, or about the multi-step calibration of astrophysical objects. To act as an independent arbiter, scientists turned to two phenomena predicted by Georges Lemaître and Edwin Hubble: gravitational waves from merging compact objects and the curvature of spacetime that creates gravitational lenses.
The new method combines two techniques, each a triumph of modern astrophysics. The first is 'standard sirens': gravitational waves from merging black holes and neutron stars, detected by LIGO, Virgo, and KAGRA. The wave amplitude directly gives the distance to the source, without needing a calibration ladder, as predicted back in 1986 by Rainer Weiss, one of LIGO's founders. From the GWTC-4 catalog, 142 events (mainly black hole mergers) were selected with a false alarm rate below 0.25 per year. For those without an electromagnetic counterpart ('dark sirens'), the redshift is estimated statistically using galaxy catalogs and population properties. The second technique is strong gravitational lensing: massive galaxies distort light from background quasars, creating multiple images that arrive with different time delays. This delay depends on the geometry of the Universe and allows the computation of a distance combination known as the time-delay distance. The combination is achieved through the 'distance sum rule'—a geometric relation valid in the Friedmann–Lemaître–Robertson–Walker metric, without assumptions about the Universe's specific content. Gravitational waves calibrate absolute distances, and lenses provide a geometric 'scaffold,' allowing H₀ to be extracted.
The analysis, performed with Bayesian tools, yielded H₀ = 83.78⁺¹²·⁵³₋₁₀·₂₃ (km/s)/Mpc with a relative precision of 13.6% when using the FullPop-4.0 population model and only two lenses: RX J1131-1231 and WGD 2038-4008. Although the central value is shifted higher than those from Planck and SH0ES, the 68% intervals overlap with all key measurements, both 'early' and 'late.' Interestingly, when the conservative hierarchical lensing treatment (accounting for mass-sheet degeneracy uncertainties) is replaced with the simpler H0LiCOW method, precision improves to 5.6% (H₀ = 75.4 ± 4.2). This underscores that the current precision bottleneck is not gravitational-wave event statistics but systematic uncertainties in lens modeling. Adding external lens samples SLACS and SL2S barely improved the precision, only shifting the central value to 88. The reason is a significant internal scatter in the mass-sheet transformation parameter among SLACS lenses, uncovered using new JWST and VLT spectroscopic data.
The work demonstrates that a model-independent method can already provide meaningful constraints on the Hubble constant. Although the current precision is insufficient to resolve the Hubble tension, it confirms the approach's fundamental viability. Importantly, the result relies neither on assumptions about the Universe's composition (as with the CMB) nor on multi-step calibration (as with the distance ladder). This is a genuinely 'third-party' arbitration. Moreover, the analysis revealed the critical role of strong lensing systematics, spurring deeper study of mass distribution in lensing galaxies and the role of dark matter.
The method's future lies in two directions. On the gravitational-wave side: more events from upcoming observing runs, especially at high redshifts, will expand the distance calibration and allow more lens systems to be included. On the lensing side: new systems with measured time delays, higher-quality spatially resolved stellar kinematics (thanks to JWST and Extremely Large Telescopes), and a better understanding of external convergence will reduce the impact of the mass-sheet degeneracy. The synergy of these improvements could reduce the error to a few percent and finally resolve the Hubble constant puzzle.
The methodology will impact observational cosmology and fundamental physics. It will provide an independent check for upcoming missions like Euclid and the Roman Space Telescope, and help identify systematic errors in traditional methods. Moreover, a precise H₀ value is critically important for understanding the nature of dark energy.
Immediate next steps include analyzing new gravitational-wave data (O4b and O5), searching for additional lensed quasars with measurable time delays in Rubin Observatory/LSST surveys, and developing more robust population models of compact objects to improve statistical redshift inference.
The study is directly linked to one of the most pressing unsolved problems in modern physics—the Hubble tension, which could point to unaccounted-for physics such as early dark energy, extra relativistic species, or modified gravity. It also touches on the mass-sheet problem in lensing, which limits the precision of all methods using strong lenses and is tied to understanding dark matter distribution in galaxies.
🎯 The standard siren method was proposed back in 1986, but the first 'bright' siren (GW170817 with a kilonova) was only recorded in 2017. Since then, LIGO, Virgo, and KAGRA detectors have been observing black hole mergers almost weekly. The record for the most distant of these mergers currently stands at about 9 billion light-years.
🎬 The idea of gravitational lenses as 'cosmic telescopes' often appears in science fiction. For instance, in the novel 'The Light of Distant Stars,' astronomers use lensing to peer into the Universe's past. And using gravitational waves for navigation and measuring cosmic distances recalls the concept of 'gravitational cartography' from the 'Universe of Fire' series.