The Sound Horizon and Baryon Acoustic Oscillations with a Modified Early Expansion Rate

The sound horizon at the end of the baryon drag epoch, about 147 megaparsecs, is the standard ruler of cosmology: it is stamped into the galaxy distribution as the acoustic oscillation scale and into the microwave background as the peak spacing. A sustained one percent change in the early expansion rate would move the ruler to 146.43 megaparsecs, a shift of -0.45 percent, several times the stated uncertainty of 0.26 megaparsecs. The bounce contribution on the branch allowed by nucleosynthesis is far smaller, because the sound integral is dominated by epochs long after the spin term has faded. The framework therefore neither exploits nor violates the acoustic ruler: it predicts the standard value to within a tiny fraction of the measurement error, and this paper records that prediction as a checkable statement. Computed from stated assumptions, not measured.