Strong-Lens Time-Delay Distances in a Bounced Cosmology: The Distance Combination and Its Sensitivity

Strong gravitational lens time delays measure a combination of angular diameter distances to the lens, to the source, and between them, and that combination samples intermediate redshifts where a bounce correction is partly switched on. For a representative lens at redshift 0.5 with a source at redshift 2.0, the time-delay distance changes by 0.20 percent at epsilon = 0.10; across a grid of lens and source redshifts it ranges from 0.11 to 0.24 percent. Published time-delay analyses quote per-lens precisions near 5 percent and combined expansion-rate uncertainties near 2 percent, centred in the low seventies. Matching the computed shift to the combined precision gives a tolerance amplitude of epsilon = 5.350. Time-delay cosmography is therefore moderately frame-sensitive: it cannot be ported into a bounced cosmology at face value, but recomputed it becomes an independent intermediate-redshift witness with leverage the local rungs lack. This study is computed from stated assumptions, not measured.