2023ApJ...959..134N

Tension between cosmic microwave background-based and distance ladder-based determinations of the Hubble constant H₀ motivates the pursuit of independent methods that are not subject to the same systematic effects. A promising alternative, proposed by Refsdal in 1964, relies on the inverse scaling of H₀ with the delay between the arrival times of at least two images of a strongly lensed variable source such as a quasar. To date, Refsdal's method has mostly been applied to quasars lensed by individual galaxies rather than by galaxy clusters. Using the three quasars strongly lensed by galaxy clusters (SDSS J1004+4112, SDSS J1029+2623, and SDSS J2222+2745) that have both multiband Hubble Space Telescope data and published time delay measurements, we derive H₀, accounting for the systematic and statistical sources of uncertainty. While a single time delay measurement does not yield a well-constrained H₀ value, analyzing the systems together tightens the constraint. Combining the six time delays measured in the three cluster-lensed quasars gives H₀ = 74.1 ± 8.0 km s^–1 Mpc^–1. To reach 1% uncertainty in H₀, we estimate that a sample size of order of 620 time delay measurements of similar quality as those from SDSS J1004+4112, SDSS J1029+2623, and SDSS J2222+2745 would be needed. Improving the lens modeling uncertainties by a factor of two and a half may reduce the needed sample size to 100 time delays, potentially reachable in the next decade.