Determining the Hubble Constant without the Sound Horizon: A $3.6\%$ Constraint on $H_0$ from Galaxy Surveys, CMB Lensing and Supernovae

Many theoretical resolutions to the so-called "Hubble tension" rely on modifying the sound horizon at recombination, $r_s$, and thus the acoustic scale used as a standard ruler in the cosmic microwave background (CMB) and large scale structure (LSS) datasets. As shown in a number of recent works, these observables can also be used to compute $r_s$-independent constraints on $H_0$ by making use of the horizon scale at matter-radiation equality, $k_{\rm eq}$, which has different sensitivity to high redshift physics than $r_s$. As such, $r_s$- and $k_{\rm eq}$-based measurements of $H_0$ (within a $\Lambda$CDM framework) may differ if there is new physics present pre-recombination. In this work, we present the tightest constraints on the latter from current data, finding $H_0=64.8^{+2.2}_{-2.5}$ at 68% CL (in $\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ units) from a combination of BOSS galaxy power spectra, Planck CMB lensing, and the newly released Pantheon+ supernova constraints, as well as physical priors on the baryon density, neutrino mass, and spectral index. The BOSS and Planck measurements have different degeneracy directions, leading to the improved combined constraints, with a bound of $H_0 = 67.1^{+2.5}_{-2.9}$ ($63.6^{+2.9}_{-3.6}$) from BOSS (Planck) alone. The results show some dependence on the neutrino mass bounds, with the constraint broadening to $H_0 = 68.0^{+2.9}_{-3.2}$ if we instead impose a weak prior on $\sum m_\nu$ from terrestrial experiments, or shifting to $H_0 = 64.6\pm2.4$ if the neutrino mass is fixed to its minimal value. Even without dependence on the sound horizon, our results are in $\approx 3\sigma$ tension with those obtained from the Cepheid-calibrated distance ladder, which begins to cause problems for new physics models that vary $H_0$ by changing acoustic physics or the expansion history immediately prior to recombination.