A Bound on Uniform Distance Rescaling from Time Delays: What Lensing Can and Cannot Say about a Bounced Early Universe

In a cosmology where collapse halts at the Aldred density for neutron matter, 9.72e+54 g per cubic centimetre, the early universe bounces rather than beginning at a singularity. If that epoch left a uniform rescaling of all comoving distances, by a factor one plus epsilon, time delays alone could not detect it, because delay distances and Fermat delays rescale together. Combining the lensing Hubble constant with a local distance-ladder value, which does not traverse the same rescaling in the same way, bounds the parameter: the central value is -0.0035 with standard uncertainty 0.0283, giving a ninety-five per cent bound of 0.059 on the absolute rescaling. No evidence for a nonzero rescaling is found. The negative result is the result: the frame's early-universe modification, if it acts as a uniform distance rescaling, is confined below the four-per-cent level by data that already exist. Computed from published values; not measured.