A calibration-free null test from anisotropic BAO

TL;DR

This paper introduces a new, calibration-free null test for flat FLRW geometry using anisotropic BAO measurements, enabling internal consistency checks of cosmological models without relying on the absolute BAO scale.

Contribution

It derives a novel null test based solely on BAO shift parameters that does not depend on the sound horizon calibration, and reconstructs the deceleration parameter directly from anisotropic BAO data.

Findings

No evidence for deviation from flat FLRW geometry in DESI DR2 data.

The null test is independent of the absolute BAO scale.

Provides a new internal consistency check for cosmological models.

Abstract

Baryon acoustic oscillation (BAO) analyses usually report the anisotropic shift parameters $\alpha_\perp(z)$ and $\alpha_\parallel(z)$ 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-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 $r_{\rm d}/r^{\rm fid}_{\rm d}$ 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.