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