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 DR12 galaxy power spectra using
perturbation theory with $\Omega_m$ priors from Pantheon supernovae but no
priors on $\Omega_b$, we obtain constraints on $H_0$ from the second scale,
finding $H_0 =
65.1^{+3.0}_{-5.4}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$; this
differs from the best-fit of SH0ES at 95\% confidence. Similar results are
obtained if $\Omega_m$ is constrained from uncalibrated BAO: $H_0 =
65.6^{+3.4}_{-5.5}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$. Adding the
analogous lensing results from Baxter \& Sherwin 2020, the posterior shifts to
$70.6^{+3.7}_{-5.0}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$. 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 $H_0$ 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
$\sigma_{H_0} \simeq 1.6\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ in the
era of Euclid.
