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 $r_s$. In this work, we present the tightest $k_{\rm eq}$-based constraints on the expansion rate from current data, finding $H_0=64.8^{+2.2}_{-2.5}$ at 68$\%$ CL 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 (in $\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ units). 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 rather than assuming $\sum m_\nu