  The value of the Hubble constant determined from CMB and BAO measurements is
directly dependent on the sound horizon at the photon-baryon decoupling. There
has been significant interest in the possibility of new physics at the epoch
around recombination that could reduce the sound horizon and increase the
inferred value of $H_0$, thus helping to relieve the Hubble tension. One way to
determine if new physics is required would be to measure $H_0$ from BAO and CMB
without assuming any model for computing the sound horizon. In this study, we
use the recently released DESI Year 1 BAO data combined with the CMB acoustic
scale $\theta_\star$ and the Planck $\Lambda$CDM prior on $\Omega_{\rm m} h^2$
to determine $H_0$ while treating the sound horizon at baryon decoupling
$r_{\rm d}$ as a free parameter. We find $H_0=69.88 \pm 0.93$ km/s/Mpc, which
is $\sim2\sigma$ larger than $H_0 = 67.44 \pm 0.47$ km/s/Mpc in the
Planck-best-fit $\Lambda$CDM where $r_{\rm d}$ is derived using the standard
recombination model. For comparison, we perform the same analysis using the
pre-DESI BAO data with $\theta_\star$ and the same prior on $\Omega_{\rm m}
h^2$, finding $H_0= 67.37 \pm 0.96$ km/s/Mpc. This difference derives from the
notably larger value of the product $r_{\rm d}H_0$ measured by DESI. Future BAO
data from DESI will help determine if the cosmological model at the epoch of
recombination model requires a modification.
