Crosschecking Cosmic Distances from DESI BAO and DES SNe

We perform a consistency check of DESI DR2 BAO constraints ($D_M/r_d, D_H/r_d)$ by reconstructing the same quantities from DES supernovae (SNe) in bins with the same effective redshift $z_{\textrm{eff}} \in \{ 0.510, 0.706, 0.934 \}$ and a Planck $r_d$ prior. Through mock analysis we show that $D_M(z_{\rm eff})$ and $D_{H}(z_{\rm eff})$ can be locally reconstructed model agnostically from $\Lambda$CDM and extended models, but only if one employs frequentist methods; purely Bayesian reconstructions from Markov Chain Monte Carlo (MCMC) exhibit bias. We find that the ratio of the three $D_M/r_d$ values at different $z_{\textrm{eff}}$ are consistent with a horizontal, thus confirming that the distance duality relation holds up to calibration. However, the $D_H/r_d$ ratio shows a decreasing trend driven by the $z_{\textrm{eff}} = 0.934$ bin, the significance of which varies from $2.5 \sigma$ with Bayesian methods down to $1.4 \sigma$ with frequentist methods. We show that replacing DES with DES-Dovekie SNe reduces the significance to $1.7 \sigma$ and $1.2 \sigma$ in Bayesian and frequentist approaches, respectively. We conclude that distances reconstructed from SNe show good agreement with DESI BAO distances across the redshifts studied. We also note that $D_M(z_{\rm eff} = 0.510)/r_d$ reconstructed from SNe favours DESI BAO over transversal BAO against a backdrop of a $3.7 \sigma$ disagreement.