A calibration-free null test from anisotropic BAO

Abstract

Baryon acoustic oscillation (BAO) analyses usually report the anisotropic shift parameters $\hat{I}{\pm }_{\perp }(z)$ and $\hat{I}{\pm }_{\parallel }(z)$ 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-Lemaître-Robertson-Walker (FLRW) geometry written entirely in terms of the reported BAO shift parameters. The test is calibration free: the sound-horizon ratio $r_{\mathrm{d}}/r_{\mathrm{d}}^{\mathrm{fid}}$ 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.

6 pages, 4 figures