Determining the Hubble Constant without the Sound Horizon: Measurements from Galaxy Surveys

Abstract

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 $H_0=65.1_{-5.4}^{+3.0}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$; this differs from the best-fit of SH0ES at 95\% confidence. Similar results are obtained if ${\Omega }_m$ is constrained from uncalibrated BAO: $H_0=65.6_{-5.5}^{+3.4}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. Adding the analogous lensing results from Baxter \& Sherwin 2020, the posterior shifts to $70.6_{-5.0}^{+3.7}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. 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.

8 pages, 4 figures, accepted by Phys. Rev. D

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