The Transverse Baryon Acoustic Oscillation Scale in a Bounced Cosmology: Angular Diameter Distances Against Survey Values

The transverse baryon acoustic oscillation measurement compares an angular scale on the sky with the comoving distance to the tracer redshift, and in a bounced cosmology that distance carries an integrated memory of the early correction. At epsilon = 0.10 the ratio of transverse distance to sound horizon, D_M/r_d, changes by 4.34 percent at redshift 0.5, 3.82 percent at redshift 1.0, and 3.08 percent at redshift 2.0, because the distance and the horizon respond to the bounce with opposite signs and different weights. Published DESI and Sloan survey precisions on this ratio are near one percent in the best redshift bins. Matching the computed shifts to those precisions gives an amplitude tolerance of epsilon = 0.028 at redshift 1, the single most restrictive transverse bin. The transverse acoustic scale is thus a genuine bounce detector, unlike the local rungs, and its redshift pattern distinguishes an early-switching correction from a change in the late-time expansion. This study is computed from stated assumptions, not measured.