--- title: DESI DR2 BAO Measurements url: https://www.emergentmind.com/topics/desi-dr2-bao type: topic --- # DESI DR2 BAO Measurements 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 \(z_{\rm eff}=2.33\) [2503.14738]. 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 [2503.14738]. ## 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 [2503.14738]. The samples span galaxy, quasar, and Lyman-\(\alpha\) forest tracers, and are arranged to maximize redshift leverage for expansion-history constraints. | Tracer | \(z\)-range | \(z_{\rm eff}\) | |---|---:|---:| | 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-\(\alpha\) forest | 1.80–4.20 | 2.330 | The corresponding tracer counts are \(1.19\) M for BGS, \(1.05\) M for LRG1, \(1.61\) M for LRG2, \(4.54\) M for LRG3+ELG1, \(3.80\) M for ELG2, \(1.46\) M for QSO, and \(1.29\) M for the Lyman-\(\alpha\) forest [2503.14738]. 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 \(V_{\rm eff}\) ranging from \(2.7\) to \(14.8\) \(({\rm Gpc}/h)^3\) across tracers [2503.14742]. 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 [2503.14738], whereas external analyses that ingest the public DESI tables often work with thirteen independent “points” spanning \(z_{\rm eff}\approx0.07\) to \(2.4\), drawn from Bright Galaxies, three LRG bins, two ELG bins, quasars, and Lyman-\(\alpha\) auto- and cross-correlations [2507.00835]. 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, \[ D_V(z)=\bigl[(1+z)^2D_A^2(z)\,\frac{cz}{H(z)}\bigr]^{1/3}, \qquad D_M(z)=(1+z)\,D_A(z), \qquad D_H(z)=\frac{c}{H(z)}, \] and the sound horizon \[ r_d=\int_{z_d}^{\infty}\frac{c_s(z)}{H(z)}\,dz \] at the drag epoch \(z_d\) [2503.14738]. The BAO fits are usually expressed through dilation parameters \[ \alpha_\perp=\frac{D_M(z)\,r_d^{\rm fid}}{D_M^{\rm fid}(z)\,r_d}, \qquad \alpha_\parallel=\frac{D_H(z)\,r_d^{\rm fid}}{D_H^{\rm fid}(z)\,r_d}, \] with the isotropic combination \[ \alpha_{\rm iso}=(\alpha_\perp^2\alpha_\parallel)^{1/3}, \] which is equivalent to \(D_V(z)/r_d\) [2503.14738]. 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 [2503.14738]. The post-reconstruction two-point correlation function \(\xi(s,\mu)\) is measured with the Landy–Szalay estimator and decomposed into Legendre multipoles \((\ell=0,2)\); covariances are computed with the RascalC semi-analytic method, including survey geometry and non-Gaussian corrections [2503.14738]. 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 [2503.14742]. For the Lyman-\(\alpha\) forest, DR2 measures both auto-correlation and quasar cross-correlation. The analysis uses HEALPix-based splits, \(50\times50\) bins in \((r_\perp,r_\parallel)\), 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 [2503.14739]. 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 \(D_V/r_d\) or anisotropic pairs such as \(D_M/r_d\) and \(H\,r_d\); at higher redshift, public summaries used in external likelihoods often recast the same information as \(D_M/r_d\) and \(D_H/r_d\) [2503.14738]. For example, one public-data reuse reports entries such as \(z_{\rm eff}=0.07\) with \(D_V/r_d=18.85\pm0.26\), \(z_{\rm eff}=1.52\) with \(D_M/r_d=25.05\pm0.40\) and \(D_H/r_d=27.80\pm0.60\), and \(z_{\rm eff}=2.33\) with \(D_M/r_d=37.21\pm1.02\) and \(D_H/r_d=8.73\pm0.24\) [2507.00835]. The likelihood is Gaussian in the compressed distance vector. A widely reused form is \[ \chi^2_{\rm BAO}=\Delta D^T\,C^{-1}\,\Delta D, \qquad \Delta D_i\equiv D_i^{\rm model}/r_d-D_i^{\rm obs}/r_d, \] with the inverse covariance \(C^{-1}\) taken directly from the released machine-readable DR2 covariance matrix [2507.00835]. 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 [2503.23225]. 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 [2503.23225]. ## 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 \(\alpha_{\rm iso}=0.9980\pm0.0020\) for BGS, \(\alpha_{\rm iso}=0.9971\pm0.0017\) and \(\alpha_{\rm AP}=0.9941\pm0.0060\) for LRG1, \(\alpha_{\rm iso}=1.0004\pm0.0010\) and \(\alpha_{\rm AP}=1.0001\pm0.0037\) for the combined LRG3+ELG1 sample, and \(\alpha_{\rm iso}=0.9943\pm0.0023\) and \(\alpha_{\rm AP}=1.0049\pm0.0091\) for QSO [2503.14742]. Detection significances exceed \(5\sigma\) for all tracers, reaching \(\sim20\sigma\) for the most powerful LRG bins, and DR2 uncertainties are roughly half those of DR1 in representative cases such as LRG2 [2503.14742]. 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 \(\alpha\) are typically within \(1\sigma\), configuration- versus Fourier-space estimates agree to \(\le 0.6\sigma\), and alternate fiducial cosmologies produce \(\alpha\) shifts \(<0.5\sigma\) [2503.14742]. The DR2 cosmology paper states that the total BAO systematic error of \(0.1\)–\(0.2\%\) is always subdominant to statistical errors, and that tests of correlated systematics across redshift bins up to \(50\%\) correlation show negligible impact on cosmological constraints [2503.14738]. The high-redshift Lyman-\(\alpha\) anchor is validated separately with updated synthetic datasets. DR2 doubles the number of Lyman-\(\alpha\) forest spectra relative to DR1, uses \(400\) realizations rather than \(150\), and introduces CoLoRe-QL mocks with a quasi-linear input power spectrum to incorporate nonlinear BAO broadening [2503.14741]. The final Ly\(\alpha\) BAO measurement at \(z_{\rm eff}=2.33\) includes a theoretical systematic term for the BAO shift for the first time, yielding \[ D_H/r_d = 8.632 \pm 0.098\,({\rm stat}) \pm 0.026\,({\rm sys}), \qquad D_M/r_d = 38.99 \pm 0.52\,({\rm stat}) \pm 0.12\,({\rm sys}), \] with a combined \(0.65\%\) precision on the isotropic BAO scale [2503.14739]. ## 5. Cosmological constraints and dark-energy implications The official DR2 cosmology analysis finds that the BAO measurements are well described by a flat \(\Lambda\)CDM model, but that the parameters preferred by BAO are in mild, \(2.3\sigma\) tension with those determined from the CMB, while remaining consistent with the Planck acoustic angular scale \(\theta_*\) [2503.14738]. For flat \(\Lambda\)CDM, BAO alone give \[ \Omega_m = 0.2975 \pm 0.0086, \qquad H_0\,r_d=(101.54\pm0.73)\,{\rm Mpc}, \] whereas a joint DESI+CMB fit yields \[ \Omega_m=0.3027\pm0.0036, \qquad H_0=68.17\pm0.28\,{\rm km\,s^{-1}Mpc^{-1}} \] [2503.14738]. Allowing time evolution in the dark-energy equation of state with the CPL form \(w(a)=w_0+w_a(1-a)\) relaxes the BAO–CMB tension. With DESI BAO plus minimal early-Universe priors, the reported constraints are \[ w_0=-0.43\pm0.22, \qquad w_a=-1.72\pm0.64, \] rejecting \(\Lambda\)CDM at \(2.4\sigma\); adding full Planck+ACT CMB strengthens this to \[ w_0=-0.42\pm0.21, \qquad w_a=-1.75\pm0.58, \] a \(3.1\sigma\) preference for evolving dark energy [2503.14738]. When recent supernova compilations are included, the preference for dynamical dark energy over \(\Lambda\)CDM ranges from \(2.8\) to \(4.2\sigma\), depending on the SN sample [2503.14738]. The same dataset also yields strong neutrino-mass limits. For flat \(\Lambda\)CDM+\(\sum m_\nu\), DESI+CMB gives \[ \sum m_\nu < 0.064~{\rm eV}\quad(95\%~{\rm CL}), \] while in the \(w_0w_a\) extension this relaxes to \(\sum m_\nu<0.163\) eV [2503.14738]. Related CMB+DESI DR2 analyses report closely comparable upper bounds, though they note some sensitivity to the exact CMB likelihood combination [2504.18464]. A second misconception concerns the status of the dark-energy signal. DR2 BAO alone do not require departure from \(\Lambda\)CDM 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 [2503.14738]. Model-independent consistency tests with Pantheon+ and Union3 using Crossing Statistics find that DESI DR2 BAO and SN Ia remain mutually consistent at the \(1\)–\(2\sigma\) level even when up to two additional smooth deformation modes are introduced [2604.19393]. ## 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 \(\Lambda\)CDM; in flat \(\Lambda\)CDM they report \( \Omega_m = 0.3035 \pm 0.0085\), \( h = 0.6876 \pm 0.0059\), and \( \sigma_8 = 0.822 \pm 0.034\) [2602.18761]. Low-redshift-agnostic compressions replace \(D_M/r_d\) nodes with adjacent increments \(\Delta D_M/r_d\), removing one absolute transverse mode below the first BAO node; applied to DESI DR1 and DR2, this yields piecewise-constant dark-energy-density parameters \(X_j\) that are all consistent with \(X=1\) within current uncertainties [2604.06888]. DR2 has also been extended to new tracers. A measurement of BAO in the C IV forest cross-correlated with quasars and ELGs finds \(D_V/r_d(z_{\rm eff}=1.92)=30.3\pm0.9\) for CIV\(\times\)QSO and \(D_V/r_d(z_{\rm eff}=1.47)=24.6\pm1.0\) for CIV\(\times\)ELG, with the new point at \(z=1.92\) lying on the best-fit \(\Lambda\)CDM expansion history from DESI DR2 galaxy+quasar BAO [2601.08103]. 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 \(w_0w_a\) fits can show internal inconsistencies across \(r_d\)-dependent and ratio observables, with large negative \(w_a\) compensating high-redshift behavior and inflating \(\Omega_m\) [2506.18230]. 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 [2503.14743; 2504.06118]. 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-\(\alpha\) forest. Its principal scientific significance lies not in a single inferred model, but in the fact that percent-level distance measurements over \(0.1