Crosschecking Cosmic Distances from DESI BAO and DES SNe

We perform a consistency check of DESI DR2 BAO constraints ($D_M\mathrm{/}{r}_d,D_H\mathrm{/}{r}_d)$ by reconstructing the same quantities from DES supernovae (SNe) in bins with the same effective redshift $z_{\text{eff}}\in \{0.510,0.706,0.934\}$ and a Planck $r_d$ prior. Through mock analysis we show that $D_M(z_{\mathrm{e}\mathrm{f}\mathrm{f}})$ and $D_H(z_{\mathrm{e}\mathrm{f}\mathrm{f}})$ can be locally reconstructed model agnostically from $\mathrm{\Lambda }$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 $D_M\mathrm{/}{r}_d$ values at different $z_{\text{eff}}$ are consistent with a horizontal, thus confirming that the distance duality relation holds up to calibration. However, the $D_H\mathrm{/}{r}_d$ ratio shows a decreasing trend driven by the $z_{\text{eff}}=0.934$ 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 $D_M(z_{\mathrm{e}\mathrm{f}\mathrm{f}}=0.510)\mathrm{/}{r}_d$ reconstructed from SNe favours DESI BAO over transversal BAO against a backdrop of a $3.7\sigma$ disagreement.