Baryon acoustic oscillation (BAO) analyses usually report the anisotropic shift parameters α⊥(z) and α∥(z) relative to a fiducial cosmology, and these quantities are primarily used for cosmological parameter inference. Here we show that they can also be used to construct a direct internal consistency test of the background geometry. In particular, we derive a new null test of flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry written entirely in terms of the reported BAO shift parameters. The test is calibration free: the sound-horizon ratio rd/rdfid cancels identically, so the relation is independent of the absolute BAO scale. We also derive a calibration-free reconstruction of the deceleration parameter q(z) from the radial BAO sector. Applying these results to anisotropic DESI DR2 BAO measurements, we find no evidence for a breakdown of the flat-FLRW distance relation within current uncertainties. Our results show that anisotropic BAO measurements already provide a nontrivial internal geometric consistency test before performing any model fit.
@article{arxiv.2603.18986,
title = {A calibration-free null test from anisotropic BAO},
author = {Domenico Sapone and Savvas Nesseris},
journal= {arXiv preprint arXiv:2603.18986},
year = {2026}
}