A calibration-free null test from anisotropic BAO

Abstract

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

Figures (4)

• Figure 1: Anisotropic BAO shift parameters from DESI DR2. Blue points denote the binned measurements of $\alpha_\perp(z)$ (top) and $\alpha_\parallel(z)$ (bottom). The black curves show a smooth two-parameter fit to $\ln\alpha_\perp$ and $\ln\alpha_\parallel$, with the shaded region indicating the propagated $68.3\%$ uncertainty.
• Figure 2: Top: reconstruction of the flat-FLRW null test $\mathcal{C}(z)$ from anisotropic BAO data. Bottom: integrated version $\mathcal{C}_{\rm int}(z)$. In both cases the dashed red line indicates the null expectation.
• Figure 3: Calibration-free reconstruction of the deceleration parameter $q(z)$ from the radial BAO sector. The dashed red line marks zero and the fiducial model; the green curve and black line show the DESI best fit and the $\alpha$-fit reconstruction respectively, with the shaded regions indicating the $68.3\%$ confidence interval.
• Figure 4: BAO-based reconstruction of $w(z)$. The dashed red line marks $w=-1$; the green curve and black line show the DESI best fit and the $\alpha$-fit reconstruction respectively, with the shaded regions indicating the $68.3\%$ confidence interval.