Quasar Lensing Distances

Strongly lensed quasars offer a distance probe that combines the geometry of gravitational lensing with the variability of the quasar source. The flux ratios and time delays between the lensed images constrain the so-called "Fermat potential" difference, which encodes the ratio of angular diameter distances between observer, lens, and source. When analyzed with detailed models of the lens mass distribution, these constraints yield H₀ independently of all stellar distance indicators. Early analyses by the H0LiCOW team, based on six systems, gave H₀ ~ 73.3 km/s/Mpc. Subsequent TDCOSMO analyses, using more flexible ("free-form") mass models that reduce assumptions about the lens profile, returned larger uncertainties and somewhat lower central values, though still above 70 km/s/Mpc.

A fundamental unresolved issue is the mass-sheet degeneracy: adding a uniform sheet of mass along the line of sight rescales all distance combinations in a way that cannot be broken from the images alone, introducing a multiplicative factor κ that directly shifts the inferred H₀. Estimates of the line-of-sight mass distribution come from galaxy number counts and weak lensing, but these corrections carry their own uncertainties. The tension here is that the best-fit H₀ from quasar lensing depends significantly on which lens model family is assumed, and ΛCDM's concordance cosmology does not uniquely predict the mass distribution of lens galaxies at the precision needed to break this degeneracy. The method's promise as a clean geometric probe is partially undermined by the galaxy formation physics that ΛCDM itself does not predict with sufficient fidelity.