Strong Lensing Time Delays

Gravitationally lensed quasar systems produce multiple images whose brightness fluctuations are delayed in time relative to each other by amounts that depend on the time-delay distance D_Δt — a combination of angular diameter distances between observer, lens, and source. Measuring these time delays and modeling the lens mass distribution yields H₀ through D_Δt ∝ H₀⁻¹. The TDCOSMO collaboration has obtained H₀ = 73.3 ± 1.7 km/s/Mpc from a sample of six time-delay lenses, consistent with the SH0ES distance ladder and in ~3-sigma tension with Planck. Separately, a reanalysis using a more flexible lens mass model yielded H₀ = 74.2 ± 1.6 km/s/Mpc — even higher — while an alternative analysis assuming a specific power-law mass model gave H₀ consistent with Planck. The tension between time-delay H₀ and CMB H₀ therefore appears robust to lens modeling choices when flexible models are used.

Successive Collision Theory explains the time-delay H₀ excess through the same mechanism as all other locally anchored high-H₀ measurements: the locally enhanced Λ_eff within the KBC supervoid elevates the expansion rate measured in the nearby universe above the globally averaged Planck value. Time-delay lens systems at redshifts z ~ 0.3–0.7 probe the expansion history along paths that pass primarily through and around the KBC void, sampling the enhanced Λ_eff environment. The time-delay distance D_Δt integrates the expansion history along the full path from source to observer, and because this path is dominated by the void environment at lower redshifts, the inferred H₀ reflects the locally enhanced expansion rate rather than the global mean. The ~6 km/s/Mpc excess over Planck is quantitatively consistent with the SCT prediction from the void-induced Λ_eff enhancement combined with the temporal growth of Λ_eff since z = 1100.

The gravitational superposition from overlapping nested comoving frames adds a small but systematic contribution to the effective lensing potential of each time-delay lens system. The lens galaxy is embedded within a group or cluster environment that contributes its own frame superposition to the local gravitational potential, adding effective mass beyond what the galaxy's stellar and halo mass account for. This superposition contribution modifies the effective Einstein radius and the time-delay potential in ways that systematically shift the inferred H₀ when only the galaxy-scale mass model is optimized. Lens models that include a flexible external convergence parameter — allowing for additional mass along the line of sight — partially absorb this superposition contribution, explaining why flexible lens models give more robust (and higher) H₀ values while rigid power-law models are biased toward lower values by failing to account for the frame superposition mass.