A New Consistency Test for the $Λ$CDM Model using Radial and Transverse BAO Measurements

TL;DR

The paper introduces a calibration-free consistency test for spatially flat $\Lambda$CDM based on ratios of BAO distances that cancel the sound horizon scale $r_{\rm d}$. By mapping each observed ratio to an effective ${\Omega}_{\rm M}^{\Lambda}$, the authors assess whether this parameter remains constant across redshift and ratio types, providing a null test of flat $\Lambda$CDM. Applying the method to DESI DR1 and DR2, they find ${\Omega}_{\rm M}^{\Lambda}$ values broadly consistent with a redshift-independent constant, with mild, non-significant deviations in some mixed-ratio tests. The approach leverages a redshift-matching scheme for integrated distances and propagates full covariance, offering a transparent, scalable consistency check that can be strengthened with future BAO data and generalized to broader cosmological models.

Abstract

We present a calibration-free consistency test of spatially flat $Λ$CDM based on baryon acoustic oscillation (BAO) distance measurements. The method forms ratios of BAO distances -- the Hubble distance $Ð(z)$, the comoving angular diameter distance $\DM(z)$, and the volume-averaged distance $\DV(z)$ -- so that the sound horizon scale cancels, and then maps each observed ratio to an effective flat-$Λ$CDM matter density parameter, $\OmL$, defined as the value of $Ω_{\rm M}$ that reproduces the measured ratio within $Λ$CDM. Flat $Λ$CDM predicts that $\OmL$ should be independent of redshift and of the particular ratio used. For ratios involving the integrated distances $\DM$ and $\DV$, we associate them with well-defined effective line-of-sight redshift intervals using a redshift-matching strategy based on the integral mean value theorem. We apply the test to BAO measurements from the Dark Energy Spectroscopic Instrument (DESI) Data Release~1 and Data Release~2, propagating the full published BAO covariance matrices into all derived ratios and $\OmL$ constraints. Within current uncertainties, the inferred $\OmL$ values are broadly consistent with a redshift-independent constant, providing an internal consistency check of flat $Λ$CDM that can be strengthened straightforwardly as BAO measurements improve.

Figures (2)

• Figure 1: Summary of BAO distances and ratio-based ${\Omega}_{\rm M}^{\Lambda}$ null tests. Panel $(A_1)$: $D_{\rm H}/r_{\rm d}$ as a function of redshift for DESI DR1, including direct radial BAO measurements (red points), and the effective $D_{\rm H}/r_{\rm d}$ ranges converted from $D_{\rm M}/r_{\rm d}$ (blue bands) and $D_{\rm V}/r_{\rm d}$ (green bands) using the redshift-matching procedure described in Secs. \ref{['subsec:zmatch']}--\ref{['subsec:DMtoDH']}. Panel $(A_2)$: ${\Omega}_{\rm M}^{\Lambda}$ inferred from the radial--radial ratio $D_{\rm H}(z_i)/D_{\rm H}(z_j)$ (red bands). Panel $(A_3)$: ${\Omega}_{\rm M}^{\Lambda}$ inferred from the radial--transverse ratio $D_{\rm H}(z_i)/D_{\rm M}(z_i)$ (blue bands). Panel $(A_4)$: ${\Omega}_{\rm M}^{\Lambda}$ inferred from the radial--isotropic ratio $D_{\rm H}(z_i)/D_{\rm V}(z_j)$ (green bands). Panels $(B_1)$--$(B_4)$ show the corresponding results for DESI DR2. The gray band in panels (A2)--(B4) shows the Planck 2018 flat-$\Lambda$CDM constraint on $\Omega_{\rm M}$ (shown for comparison; 68% CL) Planck2018.
• Figure 2: Effective-redshift mapping implied by $D_{\rm M}(z)=z\,D_{\rm H}(z_{\rm c})$ (left) and $D_{\rm V}(z)=z\,D_{\rm H}(z_{\rm d})$ (right) in flat $\Lambda$CDM for representative values of ${\Omega}_{\rm M}$. For each $z$, the mapped redshifts satisfy $0<z_{\rm c}<z_{\rm d}<z$. Increasing ${\Omega}_{\rm M}$ shifts both $z_{\rm c}$ and $z_{\rm d}$ to lower values, so ${\Omega}_{\rm M}=1$ provides a conservative lower bound for the effective redshift associated with a given $D_{\rm M}(z)$ or $D_{\rm V}(z)$.