Determining the Hubble constant without the sound horizon: Measurements from galaxy surveys

Two sources of geometric information are encoded in the galaxy power spectrum: the sound horizon at recombination and the horizon at matter-radiation equality. Analyzing the BOSS 12th data release galaxy power spectra using perturbation theory with ₌ priors from Pantheon supernovae but no priors on ₁, we obtain constraints on H₀ from the second scale, finding H₀=65. 1-₅. ₄^+3. 0 km s^-1 Mpc^-1; this differs from the best fit of SH0ES at 95% confidence. Similar results are obtained if ₌ is constrained from uncalibrated baryon acoustic oscillations: H₀=65. 6-₅. ₅^+3. 4 km s^-1 Mpc^-1. Adding the analogous lensing results from Baxter and Sherwin from 2020, the posterior shifts to 70. 6-₅. ₀^+3. 7 km s^-1 Mpc^-1. Using mock data, Fisher analyses, and scale cuts, we demonstrate that our constraints do not receive significant information from the sound horizon scale. Since many models resolve the H₀ controversy by adding new physics to alter the sound horizon, our measurements are a consistency test for standard cosmology before recombination. A simple forecast indicates that such constraints could reach ₇₀1. 6 km s^-1 Mpc^-1 in the era of Euclid.