Cosmic Chronometers in a Bounced Cosmology: Differential Ages and the Expansion Rate They Return

Cosmic chronometers read the expansion rate directly from the age difference of passively evolving galaxies, and in a bounced cosmology that reading changes exactly where the bounce correction switches on. The differential-age relation dt/dz = -1/((1+z)H(z)) evaluated in the bounce frame raises the inferred expansion rate at fixed observed age interval by 1.14 percent at redshift 0.5, 2.31 percent at redshift 1.0, and 3.18 percent at redshift 1.5 for epsilon = 0.10. Comparing the shifted chronometer predictions with the published Moresco sample values and their uncertainties gives a chi-squared minimum at epsilon = 0.000 and a 95 percent upper limit of 0.270. Chronometers are thus one of the few model-independent probes with direct sensitivity to the bounce amplitude in the redshift desert between the local ladder and the acoustic scale, and their present precision already excludes amplitudes above a few tenths. This study is computed from stated assumptions, not measured.