Calibrating the Sound Horizon in a Bounced Cosmology: The Drag-Epoch Integral and Its Error Budget

The sound horizon at the drag epoch is the length that turns angular and redshift separations into distances, and its value is an integral over the expansion rate in the first few hundred thousand years. Evaluating that integral in a bounced cosmology, with the correction fully switched on at the relevant redshifts, shortens the horizon from 141.56 Mpc to 134.97 Mpc at epsilon = 0.10, a change of -4.65 percent. The contributions to that change are decomposed by redshift interval: the decade above the drag epoch contributes 35.8 percent of the shift, and the long tail to redshift 10^5 contributes the rest. An error budget comparing the frame shift with the terms that ordinarily dominate horizon uncertainty, the baryon density, the matter density, and the effective number of relativistic species, shows the bounce term exceeding the baryon-density term once epsilon passes 0.003. Any use of the acoustic scale in a bounced cosmology that keeps the standard-frame horizon is therefore internally inconsistent above that amplitude. This study is computed from stated assumptions, not measured.