Quasar Lensing Distances

Gravitationally lensed quasar systems provide distance information through multiple channels: the image positions and flux ratios constrain the lens mass model, the time delays between lensed images encode the time-delay distance, and statistical samples of lensing cross-sections test the cosmological volume element. Several analyses of quasar lensing statistics have found mild but persistent tensions with ΛCDM predictions: the number density of lensing systems as a function of image separation and flux ratio shows deviations from standard CDM halo profiles, and quasar lensing optical depths at various redshifts sit slightly above or below ΛCDM predictions depending on the assumed cosmological parameters. These tensions at the one-to-two sigma level compound the broader H₀ and structure growth discrepancies.

Successive Collision Theory addresses quasar lensing distance tensions through two mechanisms. First, the effective cosmological term Λ_eff(x,t) that governs the expansion history also governs the cosmological volume element dV/dz, the comoving distance D_C(z), and the lensing efficiency kernel. Because Λ_eff is dynamical and spatially varying, the predicted lensing cross-section and time-delay distance both deviate from ΛCDM's constant-Λ values at a level that grows with redshift. Lensing analyses that assume a constant Λ will systematically misfit the redshift distribution and optical depth of the observed lens population. The corrections are small at low redshift but grow toward z ~ 1–2, where most strong lensing systems are found, and their signature is a coherent tilt in the observed lens population relative to ΛCDM expectations.

Second, the gravitational superposition from overlapping nested comoving frames contributes to the effective lensing potential at each deflecting galaxy or cluster. This superposition adds effective mass above what the baryonic and discrete halo model predicts, systematically increasing the Einstein radii and time-delay distances inferred for strong lensing systems. This is the same mechanism that explains the A_lens lensing amplitude excess in the CMB. For quasar lens systems, the superposition contribution increases with the depth of the lens galaxy's embedding in the frame hierarchy, predicting that lens galaxies in dense environments will show systematically larger effective Einstein radii than isolated lenses of the same stellar mass — a correlation detectable in large lens samples from Euclid and the Vera Rubin Observatory.