DESI DR2 BAO Measurements

• The paper presents DESI DR2 BAO as a high-precision dataset offering percent-level distance measurements from over 14 million galaxies, quasars, and Lyman-α forest tracers.
• The methodology leverages iterative reconstruction with pyrecon, Legendre multipole analysis, and robust covariance estimation to extract standard FLRW distance measures.
• Its public likelihood products facilitate extensive cosmological tests, including ΛCDM verification, evolving dark energy models, neutrino mass constraints, and modified gravity investigations.

Searching arXiv for recent DESI DR2 BAO papers and related analyses. arXiv search: "DESI DR2 BAO measurements cosmological constraints" DESI DR2 BAO denotes the baryon acoustic oscillation distance measurements released from the second data release of the Dark Energy Spectroscopic Instrument, together with the associated validation analyses, covariance products, and cosmological interpretations. In DR2, DESI reports BAO constraints from more than 14 million galaxies and quasars drawn from three years of operation, and combines the galaxy and quasar measurements with companion Lyman-$\alpha$ forest BAO results to obtain a distance–redshift relation extending from low redshift to $z_{\rm eff}=2.33$ (Collaboration et al., 18 Mar 2025). The dataset is central to late-time expansion studies because it provides percent-level measurements of $D_V/r_d$, $D_M/r_d$, and $D_H/r_d$, where $r_d$ is the sound horizon at the drag epoch, and because its public likelihood products are sufficiently compressed to be reused in a wide range of cosmological analyses (Collaboration et al., 18 Mar 2025).

1. Survey content and tracer structure

DESI DR2 provides spectroscopic redshifts for seven tracer samples used for BAO measurements, with the effective redshift defined by

$$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$

where $w_i$ are pair weights (Collaboration et al., 18 Mar 2025). The samples span galaxy, quasar, and Lyman-$\alpha$ forest tracers, and are arranged to maximize redshift leverage for expansion-history constraints.

Tracer	$z$-range	$z_{\rm eff}=2.33$0
BGS	0.10–0.40	0.295
LRG1	0.40–0.60	0.510
LRG2	0.60–0.80	0.706
LRG3+ELG1	0.80–1.10	0.934
ELG2	1.10–1.60	1.321
QSO	0.80–2.10	1.484
Lyman-$z_{\rm eff}=2.33$1 forest	1.80–4.20	2.330

The corresponding tracer counts are $z_{\rm eff}=2.33$2 M for BGS, $z_{\rm eff}=2.33$3 M for LRG1, $z_{\rm eff}=2.33$4 M for LRG2, $z_{\rm eff}=2.33$5 M for LRG3+ELG1, $z_{\rm eff}=2.33$6 M for ELG2, $z_{\rm eff}=2.33$7 M for QSO, and $z_{\rm eff}=2.33$8 M for the Lyman-$z_{\rm eff}=2.33$9 forest (Collaboration et al., 18 Mar 2025). The galaxy and quasar clustering validation paper further resolves the 0.80–1.10 region into separate LRG3 and ELG1 samples before optimal combination, and reports effective volumes $D_V/r_d$0 ranging from $D_V/r_d$1 to $D_V/r_d$2 $D_V/r_d$3 across tracers (Andrade et al., 18 Mar 2025).

A common source of confusion is the relation between the seven effective cosmology bins and the public BAO vectors used in downstream work. The official DR2 cosmology presentation emphasizes the seven tracer-level effective redshifts above (Collaboration et al., 18 Mar 2025), whereas external analyses that ingest the public DESI tables often work with thirteen independent “points” spanning $D_V/r_d$4 to $D_V/r_d$5, drawn from Bright Galaxies, three LRG bins, two ELG bins, quasars, and Lyman-$D_V/r_d$6 auto- and cross-correlations (Sharma et al., 1 Jul 2025). These are different compressed views of the same release rather than incompatible datasets.

2. Distance observables and extraction methodology

The DR2 BAO program is formulated in terms of standard FLRW distance measures,

$D_V/r_d$7

and the sound horizon

$D_V/r_d$8

at the drag epoch $D_V/r_d$9 (Collaboration et al., 18 Mar 2025). The BAO fits are usually expressed through dilation parameters

$D_M/r_d$0

with the isotropic combination

$D_M/r_d$1

which is equivalent to $D_M/r_d$2 (Collaboration et al., 18 Mar 2025).

For the galaxy and quasar samples, nonlinear large-scale flows are partially reversed by the IterativeFFT reconstruction algorithm implemented in pyrecon, restoring the linear acoustic feature (Collaboration et al., 18 Mar 2025). The post-reconstruction two-point correlation function $D_M/r_d$3 is measured with the Landy–Szalay estimator and decomposed into Legendre multipoles $D_M/r_d$4; covariances are computed with the RascalC semi-analytic method, including survey geometry and non-Gaussian corrections (Collaboration et al., 18 Mar 2025). The validation analysis shows that DESI also cross-checks the reconstruction-era BAO signal in Fourier space through power-spectrum multipoles, and that the baseline template isolates wiggle and no-wiggle components with Gaussian damping and broadband marginalization (Andrade et al., 18 Mar 2025).

For the Lyman-$D_M/r_d$5 forest, DR2 measures both auto-correlation and quasar cross-correlation. The analysis uses HEALPix-based splits, $D_M/r_d$6 bins in $D_M/r_d$7, a full covariance including cross-covariance among four correlations, and a template incorporating BAO peak terms, metal contamination, high-column-density contamination, continuum-distortion effects, and redshift-space distortions (Collaboration et al., 18 Mar 2025). This yields the high-redshift anchor of the DR2 BAO ladder.

3. Public data products and likelihood construction

The public DR2 BAO products are deliberately compressed. At lower redshift the released tables provide $D_M/r_d$8 or anisotropic pairs such as $D_M/r_d$9 and $D_H/r_d$0; at higher redshift, public summaries used in external likelihoods often recast the same information as $D_H/r_d$1 and $D_H/r_d$2 (Collaboration et al., 18 Mar 2025). For example, one public-data reuse reports entries such as $D_H/r_d$3 with $D_H/r_d$4, $D_H/r_d$5 with $D_H/r_d$6 and $D_H/r_d$7, and $D_H/r_d$8 with $D_H/r_d$9 and $r_d$0 (Sharma et al., 1 Jul 2025).

The likelihood is Gaussian in the compressed distance vector. A widely reused form is

$r_d$1

with the inverse covariance $r_d$2 taken directly from the released machine-readable DR2 covariance matrix (Sharma et al., 1 Jul 2025). The same structure appears in cosmological reanalyses implemented in MontePython or Cobaya, where the observed data vector and published covariance are read directly and multiplied by other probe likelihoods such as CMB or supernovae (Silva et al., 29 Mar 2025).

In this sense, “DESI DR2 BAO” refers not only to published central values but also to a standardized likelihood object. That feature has enabled model-dependent studies of dynamical dark energy, interacting dark sectors, neutrino physics, modified gravity, and low-redshift-agnostic reconstructions without re-deriving BAO from raw spectra (Silva et al., 29 Mar 2025).

4. Validation, robustness, and systematics

A defining aspect of DR2 BAO is the extent of its validation program. The galaxy and quasar validation paper reports post-reconstruction dilation measurements such as $r_d$3 for BGS, $r_d$4 and $r_d$5 for LRG1, $r_d$6 and $r_d$7 for the combined LRG3+ELG1 sample, and $r_d$8 and $r_d$9 for QSO (Andrade et al., 18 Mar 2025). Detection significances exceed $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$0 for all tracers, reaching $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$1 for the most powerful LRG bins, and DR2 uncertainties are roughly half those of DR1 in representative cases such as LRG2 (Andrade et al., 18 Mar 2025).

Robustness tests cover configuration-space versus Fourier-space estimators, alternative broadband treatments, data splits by sky region and sample properties, imaging-weight removal, pre- versus post-reconstruction consistency, and alternate fiducial cosmologies. The reported shifts in $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$2 are typically within $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$3, configuration- versus Fourier-space estimates agree to $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$4, and alternate fiducial cosmologies produce $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$5 shifts $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$6 (Andrade et al., 18 Mar 2025). The DR2 cosmology paper states that the total BAO systematic error of $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$7–$$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$8 is always subdominant to statistical errors, and that tests of correlated systematics across redshift bins up to $$z_{\rm eff}=\frac{\sum_i\sum_j w_i w_j (z_i+z_j)/2}{\sum_i\sum_j w_i w_j},$$9 correlation show negligible impact on cosmological constraints (Collaboration et al., 18 Mar 2025).

The high-redshift Lyman-$w_i$0 anchor is validated separately with updated synthetic datasets. DR2 doubles the number of Lyman-$w_i$1 forest spectra relative to DR1, uses $w_i$2 realizations rather than $w_i$3, and introduces CoLoRe-QL mocks with a quasi-linear input power spectrum to incorporate nonlinear BAO broadening (Casas et al., 18 Mar 2025). The final Ly$w_i$4 BAO measurement at $w_i$5 includes a theoretical systematic term for the BAO shift for the first time, yielding

$w_i$6

with a combined $w_i$7 precision on the isotropic BAO scale (Collaboration et al., 18 Mar 2025).

5. Cosmological constraints and dark-energy implications

The official DR2 cosmology analysis finds that the BAO measurements are well described by a flat $w_i$8CDM model, but that the parameters preferred by BAO are in mild, $w_i$9 tension with those determined from the CMB, while remaining consistent with the Planck acoustic angular scale $\alpha$0 (Collaboration et al., 18 Mar 2025). For flat $\alpha$1CDM, BAO alone give

$\alpha$2

whereas a joint DESI+CMB fit yields

$\alpha$3

(Collaboration et al., 18 Mar 2025).

Allowing time evolution in the dark-energy equation of state with the CPL form $\alpha$4 relaxes the BAO–CMB tension. With DESI BAO plus minimal early-Universe priors, the reported constraints are

$\alpha$5

rejecting $\alpha$6CDM at $\alpha$7; adding full Planck+ACT CMB strengthens this to

$\alpha$8

a $\alpha$9 preference for evolving dark energy (Collaboration et al., 18 Mar 2025). When recent supernova compilations are included, the preference for dynamical dark energy over $z$0CDM ranges from $z$1 to $z$2, depending on the SN sample (Collaboration et al., 18 Mar 2025).

The same dataset also yields strong neutrino-mass limits. For flat $z$3CDM+$z$4, DESI+CMB gives

$z$5

while in the $z$6 extension this relaxes to $z$7 eV (Collaboration et al., 18 Mar 2025). Related CMB+DESI DR2 analyses report closely comparable upper bounds, though they note some sensitivity to the exact CMB likelihood combination (Garcia-Quintero et al., 25 Apr 2025).

A second misconception concerns the status of the dark-energy signal. DR2 BAO alone do not require departure from $z$8CDM in the same sense as the combined BAO+CMB+SN analyses; rather, the more pointed tension arises from the combination of precise BAO distances with external probes (Collaboration et al., 18 Mar 2025). Model-independent consistency tests with Pantheon+ and Union3 using Crossing Statistics find that DESI DR2 BAO and SN Ia remain mutually consistent at the $z$9–$z_{\rm eff}=2.33$00 level even when up to two additional smooth deformation modes are introduced (Woo et al., 21 Apr 2026).

6. Reanalyses, extensions, and open interpretive questions

Because the DR2 likelihood is public and compact, it has rapidly become a reference dataset for methodological extensions. Joint DESI DR1 full-shape plus DR2 BAO analyses use ShapeFit compression and mock-estimated cross-covariances to obtain reliable DESI-only Bayesian constraints beyond $z_{\rm eff}=2.33$01CDM; in flat $z_{\rm eff}=2.33$02CDM they report $z_{\rm eff}=2.33$03, $z_{\rm eff}=2.33$04, and $z_{\rm eff}=2.33$05 (Forero-Sánchez et al., 21 Feb 2026). Low-redshift-agnostic compressions replace $z_{\rm eff}=2.33$06 nodes with adjacent increments $z_{\rm eff}=2.33$07, removing one absolute transverse mode below the first BAO node; applied to DESI DR1 and DR2, this yields piecewise-constant dark-energy-density parameters $z_{\rm eff}=2.33$08 that are all consistent with $z_{\rm eff}=2.33$09 within current uncertainties (Liu et al., 8 Apr 2026).

DR2 has also been extended to new tracers. A measurement of BAO in the C IV forest cross-correlated with quasars and ELGs finds $z_{\rm eff}=2.33$10 for CIV$z_{\rm eff}=2.33$11QSO and $z_{\rm eff}=2.33$12 for CIV$z_{\rm eff}=2.33$13ELG, with the new point at $z_{\rm eff}=2.33$14 lying on the best-fit $z_{\rm eff}=2.33$15CDM expansion history from DESI DR2 galaxy+quasar BAO (Bault et al., 13 Jan 2026). This suggests that the standard-ruler interpretation of DR2 BAO is internally extensible across independent tracers.

At the same time, the interpretation of DR2 dark-energy hints remains method-dependent. Parametric CPL analyses based on DESI BAO alone have been criticized on the grounds that $z_{\rm eff}=2.33$16 fits can show internal inconsistencies across $z_{\rm eff}=2.33$17-dependent and ratio observables, with large negative $z_{\rm eff}=2.33$18 compensating high-redshift behavior and inflating $z_{\rm eff}=2.33$19 (Lee, 23 Jun 2025). By contrast, broader DESI-supported analyses using shape-function reconstructions, binning, and Gaussian Processes conclude that the preference for low-redshift evolution is stable across parametric and non-parametric approaches, while noting that possible systematic effects must still be carefully considered (Lodha et al., 18 Mar 2025, Gu et al., 8 Apr 2025).

The resulting picture is therefore technically precise but interpretively non-final. DESI DR2 BAO has established a high-precision standard-ruler dataset with validated covariance products, robust reconstruction and fitting pipelines, and extensive tracer coverage from low redshift to the Lyman-$z_{\rm eff}=2.33$20 forest. Its principal scientific significance lies not in a single inferred model, but in the fact that percent-level distance measurements over $z_{\rm eff}=2.33$21 now support both stringent $z_{\rm eff}=2.33$22CDM tests and increasingly detailed investigations of dynamical dark energy, neutrino mass, and modified-gravity alternatives (Collaboration et al., 18 Mar 2025).