Recombination-independent determination of the sound horizon and the Hubble constant from BAO

Abstract: The Hubble tension and attempts to resolve it by modifying the physics of (or at) recombination motivate finding ways to determine $H_0$ and the sound horizon at the epoch of baryon decoupling $r_{\rm d}$ in ways that neither rely on a recombination model nor on late-time Hubble data. In this work, we investigate what one can learn from the current and future BAO data when treating $r_{\rm d}$ and $H_0$ as independent free parameters. It is well known that BAO gives exquisite constraints on the product $r_{\rm d}H_0$. We show here that imposing a moderate prior on $\Omega_{\rm m} h^2$ breaks the degeneracy between $r_{\rm d}$ and $H_0$. Using the latest BAO data, including the recently released eBOSS DR16, along with a $\Omega_{\rm m} h^2$ prior based on the Planck best fit $\Lambda$CDM model, we find $r_{\rm d} =143.7 \pm 2.7$ Mpc and $H_0 = 69.6 \pm 1.8$ km/s/Mpc. BAO data therefore prefers somewhat lower $r_{\rm d}$ and higher $H_0$ than those inferred from Planck data in a $\Lambda$CDM model. We find similar values when combing BAO with the Pantheon supernovae, DES galaxy weak lensing, Planck or SPTPol CMB lensing and the cosmic chronometers data. We perform a forecast for DESI and find that, when aided with a moderate prior on $\Omega_{\rm m} h^2$, DESI will measure $r_{\rm d}$ and $H_0$ without assuming a recombination model with an accuracy surpassing the current best estimates from Planck.