Baryon Acoustic Oscillations from a Different Angle

TL;DR

The paper restructures BAO analyses by rotating the BAO distance observables into two orthogonal quantities, $\mathcal{D}^{\rm perp}$ and $\mathcal{D}^{\rm par}$, to provide a straightforward test of Planck $\Lambda$CDM consistency and to extract $\omega_m$-sensitive information. Applying this to DESI DR1 and DR2 shows DR2 BAO measurements are more consistent with Planck $\Lambda$CDM than DR1, with improved alignment across redshifts in the perpendicular direction and only mild shifts in the parallel direction. When combining BAO with a compressed CMB likelihood, a nominal $2.4\sigma$ preference for evolving dark energy arises under a two-parameter $w_0$-$w_a$ model, but the result hinges on prior choices and model comparisons, prompting a critical view of Bayesian evidences in this context. The work emphasizes that while DESI DR2 strengthens the BAO+CMB consistency with $\Lambda$CDM, the claimed EvDE signal is methodologically sensitive and not decisively established, especially given SN tensions.

Abstract

This paper presents an alternative way of analysing Baryon Acoustic Oscillation (BAO) distance measurements via rotations to define new quantities Dperp and Dpar. These quantities allow simple tests of consistency with the Planck LCDM cosmology. The parameter Dperp is determined with negligible uncertainty from Planck under the assumption of LCDM. Comparing with measurements from the Dark Energy Spectroscopic Instrument (DESI), we find that the measurements of Dperp from Data Release 2 (DR2) move into significantly better agreement with the Planck LCDM cosmology compared to DESI Data Release 1 (DR1). The quantity in the orthogonal direction Dpar provides a measure of the physical matter density omega_m in the LCDM cosmology. The DR2 measurements of Dpar remain consistent with Planck LCDM despite the substantial improvement in their accuracy compared to the earlier DR1 results. From the comparison of Planck and DESI BAO measurements, we find no significant evidence in support of evolving dark energy. We also investigate a rotation in the theory space of the w_0 and w_a parameterization of the dark energy equation-of-state w(z). We show that the combination of DESI BAO measurements and the CMB constrain w(z=0.5) = -0.996 pm 0.046, i.e. very close to the value expected for a cosmological constant. We present a critique of the statistical methodology employed by the DESI collaboration and argue that it gives a misleading impression of the evidence in favour of evolving dark energy. An Appendix shows that the cosmological parameters determined from the Dark Energy Survey 5 Year supernova sample are in tension with those from DESI DR2 and parameters determined by Planck.

Figures (5)

• Figure 1: 68% and 95% contours for the rotated BAO parameters ${\cal D}^{\rm perp}$ and ${\cal D}^{\rm par}$. We show results for the LRG1 and LRG2 surveys for the 2024 DESI DR1 and 2025 DESI DR2 analyses. Samples from the Planck base $\Lambda$CDM chains are shown by the dots: green for samples from the TT chains and purple for the TTTEEE chains. The spread along the ${\cal D}^{\rm par}$ direction is determined to high accuracy by the value of the physical matter density parameter $\omega_m = \Omega_m h^2$. The red dots show the best fit values from the Planck TTTEEE chains. The green dots show the best fit values for the DESI+($\theta_*$, $\omega_b$, $\omega_{bc})_{\rm CMB}$ fits from DESI-DR1 and DESI-DR2.
• Figure 2: Posterior distributions of ${\cal D}^{\rm perp}$ for the DESI DR1 and DR2 LRG1 and LRG2 samples. The Planck$\Lambda$CDM values (which have negligible error) are shown by the thick red lines. Note the $\sim 2.5\sigma$ tension between the Planck value and ${\cal D}^{\rm perp}$ measured from the DR1 LRG1 sample, which becomes less significant in DR2.
• Figure 3: The upper panel shows the residual $\Delta {\cal D}^{\rm perp}_{\rm DESI} - {\cal D}^{\rm perp}_{\rm Planck}$ as a function of effective redshift for the DESI DR1 and DR2 samples. Note how the DR2 measurements shift closer to the Planck values. The lower panel shows the matter density parameter $\omega_m$ inferred from the DESI measurements of ${\cal D}^{\rm par}$. The horizontal bands show the $1$ and $2\sigma$ ranges allowed by Planck for the base $\Lambda$CDM cosmology. As in the upper panel, the DR2 results move closer to the expectations of the Planck$\Lambda$CDM cosmology.
• Figure 4: The left hand panel shows 68% and 95% contours for the marginalized posterior parameters in the $w_0-w_a$, $w_0-\Omega_m$ and $w_a-\Omega_m$ planes for the Pantheon+ (red) and DES5Y (blue) SN compilations. The dashed lines show the values for the best fit Planck$\Lambda$CDM cosmology. The green dashed line shows the relation of Eq. \ref{['equ:piv2']} determined by fixing $w_{\rm piv} = w(z_{\rm piv}) = -1$ at a pivot redshift $z_{\rm piv} = 0.5$. The right hand panel shows the constraints on $w_{\rm piv}$ and $w_a$, illustrating the tight constraints on $w_{\rm piv}$ and the decorrelation of $w_{\rm piv}$ from $w_a$.
• Figure 5: 68% and 95% contours for the marginalized posterior parameters in the $w_{\rm piv}-w_a$, $w_{\rm piv}-\Omega_m$ and $w_a-\Omega_m$ planes for DES5Y (blue) SN compilations. The remaining contours show DES5Y combined with QCMB (green), DESI BAO combined with DES5YSN (red), and DESI BAO combined with DES6YSN and QCMB (dark blue). The dashed lines show the values for the best fit Planck$\Lambda$CDM cosmology.