DESI DR2 BAO Data & Cosmological Insights

• DESI DR2 BAO data are a comprehensive set of baryon acoustic oscillation measurements mapping late-time cosmic expansion from 0.1 to 4.2 in redshift.
• The dataset uses galaxy and quasar spectroscopy to extract normalized distance ratios (D_V, D_M, D_H) relative to the sound horizon for robust cosmological inference.
• High signal-to-noise observations enable stringent tests of ΛCDM and extended models, tightening constraints on dark energy parameters and neutrino masses.

The DESI DR2 BAO dataset refers to the baryon acoustic oscillation (BAO) measurements produced in the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI) survey. This dataset constitutes the most extensive and precise collection of 3D BAO distance measurements available to date, providing a cornerstone for late-time cosmological parameter inference, dark energy constraints, and consistency tests of the ΛCDM paradigm and its extensions.

1. Definition and Content of DESI DR2 BAO Data

DESI DR2 delivers spectroscopic measurements from more than 14 million galaxies and quasars, employing multiple tracers to map the BAO scale over a wide redshift range, 0.1 < z < 4.2. The key tracers and their effective redshifts are:

Tracer	z_eff	BAO Observables
BGS	0.295	D_V / r_d
LRG	0.510, 0.706	D_M / r_d, D_H / r_d
LRG+ELG	0.934	D_M / r_d, D_H / r_d
ELG	1.321	D_M / r_d, D_H / r_d
QSO	1.484	D_M / r_d, D_H / r_d
Lyα	2.330	D_M / r_d, D_H / r_d

The observed quantities are dimensionless distance ratios normalized by the comoving sound horizon at the drag epoch, r_d. These include:

• The spherically averaged distance D_V(z)/r_d.
• The transverse comoving distance D_M(z)/r_d.
• The Hubble (radial) distance D_H(z)/r_d ≡ c / [H(z) r_d].

Anisotropic fits yield D_M and D_H separately; isotropic fits (notably for BGS) provide only D_V. The full DESI DR2 release includes a joint covariance matrix for all reported observables, essential for robust likelihood construction (Collaboration et al., 18 Mar 2025).

2. Measurement Methodology and Theoretical Framework

BAO observables are extracted via fits to the reconstructed galaxy correlation functions and, for the Lyα forest, the flux correlation and quasar cross-correlation. The standard definitions, following a Friedmann–Robertson–Walker metric, are:

• D_M(z) = c ∫_0^z dz' / H(z')
• D_H(z) = c / H(z)
• D_V(z) = [ (1+z)^2 D_A^2(z) c z / H(z) ]^{1/3}
• r_d = ∫{z_d}^{∞} c_s(z)/H(z) dz, with c_s^2(z) = c^2 / [3(1+R(z))], R(z) = 3 ρ_b / (4 ργ)

The DR2 likelihood is constructed as a multivariate Gaussian in the data vector d_obs = {D_V/r_d, D_M/r_d, D_H/r_d}_i, with the full covariance C provided by DESI. At each cosmological model point θ, the corresponding theoretical values d_th(θ) are computed, and the likelihood evaluates:

$$\chi^2_{\rm BAO} = [d_{\rm obs} - d_{\rm th}(\theta)]^T\,C^{-1}\,[d_{\rm obs} - d_{\rm th}(\theta)]$$

Systematic effects, such as density‐field reconstruction and Alcock–Paczynski mapping, are accounted for by the DESI team, with any residuals entering the published covariance (Collaboration et al., 18 Mar 2025, Collaboration et al., 18 Mar 2025).

3. Influence on Cosmological Parameter Constraints

DESI DR2 BAO data are a dominant component in late-time cosmological inference, alone and in combination with other probes:

• In ΛCDM fits with DESI BAO alone: Ω_m = 0.2975 ± 0.0086 and h r_d = 101.54 ± 0.73 Mpc.
• For joint DESI BAO + Planck CMB: Ω_m = 0.3027 ± 0.0036 and H_0 = 68.17 ± 0.28 km/s/Mpc.
• In wCDM: w = –1.055 ± 0.036 with DESI+CMB.
• For extended models (w_0-w_aCDM), DESI BAO + CMB prefer (w_0, w_a) = (–0.42 ± 0.21, –1.75 ± 0.58), indicating a >3σ preference for dynamical dark energy with w_0 > –1 and w_a < 0 when combined with SNe (Collaboration et al., 18 Mar 2025, Lodha et al., 18 Mar 2025, Garcia-Quintero et al., 25 Apr 2025).

The statistical power of DR2 BAO, due to high S/N and broad redshift coverage, enables tight constraints on dark energy parameters, the sum of neutrino masses (Σm_ν < 0.064 eV at 95% CL in ΛCDM with CMB), and curvature (Ω_k), as well as testing non-standard scenarios such as lepton asymmetry, time-varying fundamental constants, and modified gravity (Zhao et al., 13 Apr 2025, Toda et al., 12 Apr 2025, Chen et al., 1 May 2025, Luciano et al., 18 Aug 2025).

4. Covariance, Systematics, and Robustness

The DR2 analysis provides a full covariance matrix for the BAO observables across all bins and tracers (typically 13×13 or larger, block-diagonal across redshift). Systematic uncertainties, including nonlinear effects at high redshift (Lyα), galaxy bias, reconstruction residuals, window functions, and survey systematics, are modeled and included explicitly; for high-z Lyα, a 0.3% theoretical systematic error is added in quadrature (Collaboration et al., 18 Mar 2025). DESI extensively cross-validated results with 1000+ mocks and performed fit-range, template, and estimator robustness tests to ensure stability of the published BAO constraints (Collaboration et al., 18 Mar 2025, Collaboration et al., 18 Mar 2025).

5. Applications in Extended Cosmological Models

The breadth and precision of DESI DR2 BAO enable stringent tests of non-ΛCDM physics:

• Constraining the lepton asymmetry: from DESI DR2 BAO + Planck, ξ_3 < 0.56 (normal) or < 0.62 (inverted) at 95% CL, robust to dynamical dark energy (Zhao et al., 13 Apr 2025).
• Modified gravity: inclusion of DESI DR2 H(z) measurements in f(Q) gravity models tightens parameter constraints by up to 50%, supporting a geometric alternative to ΛCDM acceleration (Mazumdar et al., 8 Jul 2025).
• Entropic cosmologies: joint SN+OHD+DESI DR2 analyses pin the Barrow exponent Δ close to 0, allowing only weak deviations from standard ΛCDM (Luciano et al., 16 Apr 2025, Luciano et al., 3 Jun 2025).
• Neutrino physics: the bound Σm_ν ≲ 0.064 eV (ΛCDM+DRA+Planck) is improved compared to pre-DESI limits, with partial relaxation to Σm_ν < 0.16 eV allowed in w_0w_a cosmologies or with spatial curvature (Collaboration et al., 18 Mar 2025, Chen et al., 1 May 2025).
• Tests of distance duality and consistency: when combined with SNIa (Pantheon+), DESI DR2 BAO exposes mild redshift evolution in the luminosity–angular diameter distance relation; marginalizing over such inconsistencies restores consistency with ΛCDM (Afroz et al., 23 Apr 2025).

6. Tension with Other Cosmological Probes

A ∼2σ tension persists between the DESI DR2 BAO-inferred Ω_m–H_0 parameter space and that preferred by Planck ΛCDM, with BAO distances systematically lower by ∼1.5%. This tension is alleviated in models with time-evolving dark energy crossing w = –1, or by including spatial curvature (Ω_k ≈ +0.0023 ± 0.0011) (Collaboration et al., 18 Mar 2025, Chen et al., 1 May 2025, Ye et al., 4 May 2025). Combined analyses with CMB+SNe consistently prefer dynamical dark energy (w_0 > –1, w_a < 0) over pure ΛCDM at 3–4σ (Collaboration et al., 18 Mar 2025, Lodha et al., 18 Mar 2025, Garcia-Quintero et al., 25 Apr 2025). However, attention to biases from prior-driven degeneracies and possible data-set inconsistencies remains essential (Lee, 19 Jun 2025, Afroz et al., 23 Apr 2025).

7. Summary and Data Release

The DESI DR2 BAO dataset is the definitive source for high-precision, multi-tracer, multi-redshift BAO distance measurements, with full public likelihoods and covariance matrices enabling detailed cosmological inference with minimal model dependence. The dataset comprises:

• Measurements of D_V/r_d (BGS), D_M/r_d, D_H/r_d (LRG, ELG, QSO, Lyα) over 0.1 < z < 4.2.
• Full covariance treatment and systematic uncertainties.
• Support for both model-dependent (ΛCDM, wCDM, extensions) and model-independent (inverse distance ladder, PAge, etc.) analyses.

All relevant data vectors, covariances, and codes are available from https://github.com/CobayaSampler/bao_data and the DESI public data portal. DESI DR2 BAO measurements set the current standard for late-time background expansion constraints and are expected to remain a primary geometric cosmology anchor until the completion of full DESI operations and the arrival of future high-z BAO surveys (Collaboration et al., 18 Mar 2025, Collaboration et al., 18 Mar 2025, Sabogal et al., 17 Oct 2025).