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 Ωm priors from Pantheon supernovae but no priors on Ωb, 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 Ωm 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 σH0≃1.6 km s−1 Mpc−1 in the era of Euclid.