Quantification of 2D vs 3D BAO tension using SNIa as a redshift interpolator and test of the Etherington relation

Several studies in the literature have found a disagreement between compressed data on Baryon Acoustic Oscillations (BAO) derived using two distinct methodologies: the two-dimensional (2D, transverse or angular) BAO, which extracts the BAO signal from the analysis of the angular two-point correlation function; and the three-dimensional (3D or anisotropic) BAO, which also exploits the radial clustering signal imprinted on the large-scale structure of the universe. This discrepancy is worrisome, since many of the points contained in these data sets are obtained from the same parent catalogs of tracers and, therefore, we would expect them to be consistent. Since BAO measurements play a pivotal role in the building of the inverse distance ladder, this mismatch impacts the discourse on the Hubble tension and the study of theoretical solutions to the latter. So far, the discrepancy between 2D and 3D BAO has been only pointed out in the context of fitting analyses of cosmological models or parametrizations that, in practice, involve the choice of a concrete calibration of the comoving sound horizon at the baryon-drag epoch. In this Letter, for the first time, we quantify the tension in a much cleaner way, with the aid of apparent magnitudes of supernovae of Type Ia (SNIa) and excluding the radial component of the 3D BAO. We avoid the use of any calibration and cosmological model in the process. At this point we assume that the Etherington (a.k.a distance duality) relation holds. We use state-of-the-art measurements in our analysis, and study how the results change when the angular components of the 3D BAO data from BOSS/eBOSS are substituted by the recent data from DESI Y1. We find the tension to exist at the level of $\sim 2\sigma$ and $\sim 2.5\sigma$, respectively, when the SNIa of the Pantheon+ compilation are used, and at $\sim 4.6\sigma$ when the latter are replaced with those of DES Y5. In view of these results, we then apply a calibrator-independent method to investigate the robustness of the distance duality relation when analyzed not only with 3D BAO measurements, but also with 2D BAO. This is a test of fundamental physics, which covers, among other aspects, variations of the speed of light with the cosmic expansion or possible interactions between the dark and electromagnetic sectors. We do not find any significant hint for a violation of the cosmic distance duality relation in any of the considered data sets.