From Scratch: A Direct Test of the Sound-Horizon Assumption

We evaluate the sound horizon at photon decoupling using only late-time observations and the directly measured acoustic angle from the CMB. The goal is to determine how much of the sound horizon can be recovered from data alone, without assuming any specific early-universe model. The analysis uses published cosmic-chronometer measurements of the expansion rate, the TRGB determination of the local Hubble constant, and the observed acoustic angle. A non-parametric reconstruction of the expansion history gives the distance to last scattering based solely on late-time information. This makes it possible to infer the physical sound horizon independently of the standard cosmological framework. The result is a broad estimate of the sound horizon that agrees with the commonly quoted value but carries a much larger uncertainty. Almost all of this uncertainty comes from the unobserved region between the highest redshifts reached by chronometer data and the epoch of recombination. Because no direct expansion-rate measurements exist in this range, the sound horizon cannot be sharply determined from observations alone. This evaluation shows a basic limitation in how late-time data can be used to test early-universe predictions. It also clarifies the structure behind the Hubble tension. The local determination of the Hubble constant is a direct measurement, while the CMB-derived value depends on adopting a theoretical sound horizon. The tension therefore reflects a comparison between observation and inference rather than between two independent measurements.