On the origin of the BAOtr-DESI tension

TL;DR

This paper investigates the tension between two types of BAO measurements, finding that models fitting one dataset poorly fit the other, suggesting possible observational systematics or new physics beyond the CPL model.

Contribution

It demonstrates that the observed tension cannot be resolved within the CPL parametrisation or by fiducial assumptions, highlighting a fundamental discrepancy between datasets.

Findings

Models fitting DESI data poorly fit BAOtr data and vice versa.

No CPL model can fit both datasets simultaneously at CMB-consistent parameters.

The tension at z=0.510 is irreducible and likely due to observational systematics or new physics.

Abstract

The fiducial-independent angular/transverse BAO dataset, obtained from two-point angular correlation functions in thin redshift shells (hereafter BAOtr), systematically prefers smaller comoving distance ratios $D_{\rm M}/r_{\rm d}$ than the DESI DR2 three-dimensional BAO measurements at $z \lesssim 0.65$, driving dataset-dependent CPL dark-energy inferences and conflicting conclusions about the Hubble tension. We investigate whether this disagreement can be attributed to the $\Lambda$CDM fiducial assumed in the 3D BAO pipeline, or resolved within the CPL parametrisation. We show that the published 3D BAO distances are fiducial-independent by construction, with residual effects at $\lesssim 0.3\%$ -- negligible against the 10--18\% BAOtr uncertainties. We then scan the CPL parameter space with $\Omega_m$ and $H_0$ jointly determined at each $(w_0, w_a)$ by the Planck $\theta_*$ constraint and optimisation against the DESI data. Two complementary tests are performed: a direct comparison of each DESI-optimized model with the BAOtr data, and an $\alpha$-interpolation test that anchors the prediction to the DESI measurements. Both reveal an inescapable trade-off: models that fit DESI well ($\chi^2_{\rm DESI} \lesssim 5$) yield $\chi^2_{\rm BAOtr} \gtrsim 42$, while reducing the BAOtr tension to $\chi^2_{\rm BAOtr} \sim 37$ requires $\chi^2_{\rm DESI} \gtrsim 8$. No CMB-consistent CPL model fits both datasets simultaneously. The direct comparison at $z = 0.510$ -- where BAOtr and DESI disagree by $3.7\sigma$ (data-versus-data) -- sets an irreducible tension floor that no smooth modification of $D_{\rm M}(z)$ can remove. These conclusions are robust across analysis methods, extrapolation schemes, and substitution of SDSS for DESI. The remaining explanations are observational systematics -- most plausibly in the BAOtr measurements -- or new physics beyond CPL.