Origin of the DESI low-redshift baryon acoustic oscillation distance offsets: statistical fluctuation, unmodelled systematics, or new physics

The DESI DR1 galaxy and quasar baryon acoustic oscillation (BAO) analysis found its distance measurements at z<0.8 offset from Planck-2018 Lambda-CDM predictions, and its LRG measurement at effective redshift 0.71 discrepant with the SDSS/eBOSS LRG measurement at z=0.7 at the ~2.5-3 sigma level, leaving open whether the offsets are statistical fluctuations, residual unmodelled analysis systematics, or new physics. The DESI DR2 analysis (three years of data) reduced the SDSS discrepancy to ~2.6 sigma, validated its systematics treatment, improving the combined BAO precision across the six galaxy and quasar redshift bins from 0.52% (DR1) to 0.24%, and converted the persistent low-z offsets into a 2.3 sigma Lambda-CDM parameter tension with the CMB and a 3.1 sigma preference for evolving dark energy, explicitly conditioning this conclusion on the absence of an unknown systematic. The open problem is to determine the origin of these low-redshift BAO distance offsets: demonstrate a statistical explanation at stated confidence, identify and quantify a systematic channel that reproduces the tracer- and redshift-dependent pattern, or establish a cosmological explanation consistent with all joint data.

Background

Baryon acoustic oscillations (BAO) are the imprint of sound waves in the pre-recombination photon-baryon plasma on the matter distribution: galaxies preferentially separate by the comoving sound horizon $r_d$ (about 147 Mpc in standard cosmology), providing a standard ruler with which galaxy redshift surveys measure the expansion history. A spectroscopic survey measures the transverse comoving distance $D_M(z)/r_d$ from the angular BAO scale and the Hubble distance $D_H(z)=c/H(z)$ over $r_d$ from the redshift-direction BAO scale, or their angle-averaged combination $D_V(z)/r_d$. Planck's 2018 cosmic-microwave-background (CMB) anisotropy measurements determine, within the flat Lambda-CDM model (a cosmological constant Lambda plus cold dark matter), a precise prediction for this distance-redshift relation. The Dark Energy Spectroscopic Instrument (DESI) measured BAO in its first-year data (DR1) using several tracer samples selected by color and redshift — bright galaxy sample (BGS), luminous red galaxies (LRGs), emission-line galaxies (ELGs), and quasars (QSOs) — reaching 0.52% aggregate BAO-scale precision after density-field reconstruction (a standard step that partially reverses nonlinear gravitational smearing of the BAO peak by moving galaxies back toward their more linear positions). In DESI 2024 III, the measured BAO scales at $z<0.8$ were systematically larger than the Planck-2018 Lambda-CDM prediction (implying smaller distances), most prominently at LRG1 ($z_{\rm eff}=0.51$, mainly in $D_H/r_d$) and LRG2 ($z_{\rm eff}=0.71$, mainly in $D_V/r_d$ and $D_M/r_d$: $D_M(0.71)/r_d=16.85\pm0.32$ versus $17.86\pm0.33$ from the SDSS/eBOSS LRG sample at $z_{\rm eff}=0.7$). Accounting for the small redshift difference, the DESI LRG2 and eBOSS LRG measurements disagree at close to $3\sigma$ in $D_M/r_d$ ($2.8\sigma$/$2.5\sigma$ against DESI's own reanalysis of the SDSS catalogs). The paper left the origin of these offsets unresolved, and its supporting analysis enumerated the candidate systematic channels: incomplete convergence between analytic and mock-based (EZmock) covariance matrices in Fourier space; halo occupation distribution (HOD) systematics — HOD being the model of which dark-matter halos host galaxies of each tracer class, whose variation between mock realizations shifts recovered BAO scales, with the ELG estimates limited by the available diversity of mock HOD ensembles; BAO-template assumptions such as the effective number of relativistic species $N_{\rm eff}$ (a test with $N_{\rm eff}=3.7$ produced a measurable shift, deliberately excluded from the conservative systematic budget because it concerns how the measured scale is interpreted through $r_d$); and reconstruction inefficiency for tracers with high shot noise (large Poisson sampling variance from sparsely sampling the density field), notably QSOs, whose reconstructed DESI DR1 result fell outside the mock range. DESI DR2 (three years of data, more than 14 million galaxies and quasars) found the DR2 LRG2 result lying between the DR1 and SDSS values, reducing that discrepancy to roughly $2.6\sigma$ under the most plausible survey-overlap correlation ($\sim1.9$–$2.3\sigma$ under alternative assumptions), reporting overall consistency between DR2 and SDSS, and converting the persistent low-redshift offsets into a $2.3\sigma$ tension between BAO- and CMB-preferred flat-Lambda-CDM parameters and a $3.1\sigma$ preference for dark energy with an evolving equation of state, parametrized as $w(a)=w_0+w_a(1-a)$ with present-day value $w_0>-1$ and evolution parameter $w_a<0$, from DESI BAO plus CMB — while noting that a coherent 1.5% redshift-independent systematic shift of all BAO scales would relieve the tension but would exceed the validated systematic budget by a factor of 6 to 10, and explicitly conditioning the dark-energy conclusion on the absence of an unknown systematic in one or more datasets.

Problem Statement

Determine the origin of the DESI low-redshift BAO distance offsets: (i) the systematically larger observed BAO scales (smaller distances) relative to the Planck-2018 flat-Lambda-CDM prediction at z<0.8, most prominently in $D_H/r_d$ at $z_{\rm eff}=0.51$ (LRG1) and in $D_V/r_d$ and $D_M/r_d$ at $z_{\rm eff}=0.71$ (LRG2), and (ii) the $\sim2.5$–$3\sigma$ discrepancy between the DESI DR1 LRG2 measurement and the SDSS/eBOSS LRG measurement at comparable effective redshift, which DESI DR2 reduced to a residual $\sim2.6\sigma$ under the most plausible survey-correlation assumption. A complete answer must discriminate, with quantified evidence, among the three alternatives left open by the source: (a) a statistical fluctuation, demonstrated by showing that once all validated uncertainties are propagated the offsets no longer constitute a significant anomaly under the joint likelihood — that is, an argument that lowers or removes the significance of the offsets, not a restatement of their consistency at a confidence level chosen by the answer; (b) a residual unmodelled systematic in the DESI analysis, data, or comparison — including but not limited to the channels enumerated in the source: Fourier-space covariance misspecification (analytic versus mock-based), HOD-dependent systematics for tracers with complex halo occupation such as ELGs, BAO-template assumptions such as an incorrect $N_{\rm eff}$ and their interpretation through the sound horizon $r_d$, and reconstruction inefficiency for high shot-noise tracers such as QSOs, or an analogous systematic in the SDSS/eBOSS or CMB comparison data — identified and shown to reproduce the observed tracer- and redshift-dependent pattern of offsets; or (c) new cosmological physics, namely a model distinct from the evolving-dark-energy extension and not a restatement of that extension's reported preference over flat Lambda-CDM, shown to fit the DESI BAO measurements jointly with the CMB (and, where used, supernova data) at least as well as that extension while remaining consistent with the precisely measured acoustic angular scale $\theta_*$ and other established probes. The relation among these components is that a single attribution must explain the low-redshift offset pattern as a whole across tracers and redshift bins and, where relevant, its evolution between DR1 and DR2, while the DESI-SDSS discrepancy of component (ii), being a comparison of two measurements of the same distance scale, is a separate question resolvable only through statistics or a survey-level systematic; demonstrating only one channel's plausibility without the quantitative pattern, or fitting one bin in isolation, does not answer the question.

References

1. A. G. Adame, J. Aguilar, S. Ahlen, et al. (DESI Collaboration), 'DESI 2024 III: baryon acoustic oscillations from galaxies and quasars', Journal of Cosmology and Astroparticle Physics 2025, issue 04 (2025) 012, doi:10.1088/1475-7516/2025/04/012; arXiv:2404.03000, https://arxiv.org/abs/2404.03000
2. M. Abdul Karim, J. Aguilar, S. Ahlen, et al. (DESI Collaboration), 'DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints', Physical Review D 112, 083515 (2025), doi:10.1103/tr6y-kpc6; arXiv:2503.14738, https://arxiv.org/abs/2503.14738
3. U. Andrade, E. Paillas, J. Mena-Fernández, et al. (DESI Collaboration), 'Validation of the DESI DR2 measurements of baryon acoustic oscillations from galaxies and quasars', Physical Review D 112, 083512 (2025), doi:10.1103/kdys-w8vl; arXiv:2503.14742, https://arxiv.org/abs/2503.14742
4. A. G. Adame, J. Aguilar, S. Ahlen, et al. (DESI Collaboration), 'DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations', Journal of Cosmology and Astroparticle Physics 2025, issue 02 (2025) 021, doi:10.1088/1475-7516/2025/02/021; arXiv:2404.03002, https://arxiv.org/abs/2404.03002