High-redshift physics from the acoustic scale

We present a simplified and general description of the high-redshift information in acoustic scale measurements from the cosmic microwave background and large-scale structure. The transverse distance interval between photon--baryon decoupling and a late epoch in the matter era provides an analytically tractable summary statistic thereof and a general diagnostic of the current tension between the Dark Energy Spectroscopic Instrument and the CMB. We show that this "matter-era distance excess" is unlikely to be explained by modified dynamics at low redshift. We then analytically derive the matter-era distance interval's sensitivity to new physics at high redshift, including nonstandard recombination, nonminimal dark matter dynamics, and spatial curvature; in particular, we explain how this observable represents a direct geometric measurement of (and underlies the current incompatibility with) neutrino masses. Finally, we demonstrate that phenomenological models of dynamical dark energy mediate the matter-era distance excess in a manner reliant on their unphysical, extrapolated behavior at high redshift. Invoking alternative explanations of the excess removes the CMB's contribution to the evidence for these models; the residual preference of around $1.7\sigma$ mostly derives from DESI's two lowest-redshift measurements of the Alcock--Paczynski distortion, without which it drops to $0.5 \sigma$.