DESI BAOs: High-Precision Cosmic Distance Marker

• DESI BAOs are the statistical detection and standard use of a ~150 Mpc sound horizon scale imprinted by early-universe photon–baryon interactions.
• The survey employs multi-tracer techniques and advanced reconstruction methods to achieve sub-percent precision in distance-redshift measurements over a broad redshift range.
• DESI BAO analyses tightly constrain dark energy dynamics, the Hubble constant, and neutrino properties, providing a robust test of ΛCDM and potential new physics.

Baryon Acoustic Oscillations (BAOs) measured by the Dark Energy Spectroscopic Instrument (DESI) constitute a cornerstone for high-precision cosmological inference in the 21st century. DESI BAOs refer both to the statistical detection and standardized use of the ~150 Mpc comoving-scale imprints of sound waves in the early photon–baryon fluid, which remain encoded as a preferred clustering scale in the late-time matter distribution, and to the methodologies, systematics, and cosmological implications arising from the DESI survey program. Leveraging sub-percent precision in distance-redshift measurements over $0.1 < z < 2.1$ (galaxies, quasars) and to $z \simeq 2.33$ and above ($\mathrm{Ly}\alpha$ forest), DESI’s BAO program sharply constrains the expansion history, probes the dark energy sector, and anchors the “inverse distance ladder” for $H_0$, neutrino physics, and potential deviations from ΛCDM.

1. Physical Principles and Sound Horizon Standard Ruler

BAOs originate from sound waves in the primordial baryon–photon plasma before recombination ($z\sim 1100$). The key length scale is the comoving sound horizon at the drag epoch ($r_d$), given by integrating the sound speed $c_s$ up to the baryon decoupling: $$r_d = \int_{z_d}^{\infty} \frac{c_s(z)}{H(z)} \, dz$$ where $c_s = c / \sqrt{3(1+R)}$ and $R = 3\rho_b/4\rho_\gamma$. At recombination, these perturbations are “frozen in,” imprinting a characteristic scale $\sim150$ Mpc (or $\sim105\,h^{-1}$ Mpc for $h = H_0/100\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$) in the matter correlation function. This scale enters the late-time two-point statistics as:

• A bump at $\sim$ BAO scale in $\xi(r)$:

$$\xi(r) = \langle \delta(\mathbf{x})\,\delta(\mathbf{x}+ \mathbf{r})\rangle$$

• Oscillations (“wiggles”) in the Fourier-space power spectrum $P(k)$, modulating the primordial power through $P(k) \propto e^{-ikr_d}$

Because $r_d$ is set by linear, well-understood pre-decoupling physics, BAOs act as standard rulers, enabling precise absolute measurements of $D_A(z)$ and $H(z)$ (0910.5224).

2. DESI Survey Design, Target Selection, and Data Scope

The DESI survey represents a Stage-IV spectroscopic BAO program with a robotic, fiber-fed spectrograph capable of $>5,000$ simultaneous redshift measurements per exposure. The core DESI sample, as of DR2 (Collaboration et al., 18 Mar 2025, Collaboration et al., 3 Apr 2024), consists of:

Tracer Type	Redshift Range	Number (DR2)
BGS	$0.1	$3\times10^5$
LRG	$0.4	$2.1\times10^6$
ELG	$0.8	$2.4\times10^6$
QSO	$0.8	$8.6\times10^5$
Ly$\alpha$	$z\sim2.1-3.5$	$8.2\times10^5$

Data quality control, survey footprint masking, and target selection strategies are optimized to probe BAOs through both angular and radial clustering, maximizing cosmic volume ($\sim18$ Gpc$^3$ for DR1; $>30$ Gpc$^3$ for DR2), and employing a multi-tracer strategy to allow robust cross-checks of systematics across distinct populations (Collaboration et al., 3 Apr 2024, Collaboration et al., 18 Mar 2025).

3. BAO Measurement and Statistical Pipeline

The DESI BAO pipeline is underpinned by several methodological pillars (Chen et al., 21 Feb 2024, Collaboration et al., 3 Apr 2024):

• Reconstruction: Nonlinear evolution is reversed via density-field reconstruction, solved using optimal multigrid (MG) or iterative FFT (iFFT) algorithms, shifting galaxy and random catalogs according to the linear displacement field $\Psi$. The RecSym convention (applying the same displacement to galaxies and randoms) is robust at the $<0.4\%$ level against displacement errors (Chen et al., 29 Nov 2024, Paillas et al., 3 Apr 2024).
• BAO Template Fitting: Observed clustering statistics (power spectrum or two-point correlation function) are decomposed:

$$P_{gg}(k, \mu) = \mathcal{B}(k,\mu) P_\mathrm{nw}(k) + \mathcal{C}(k,\mu) P_\mathrm{w}(k) + \mathcal{D}(k,\mu)$$

where the “wiggle” component $P_\mathrm{w}(k)$ is subject to a geometric dilation parameterization:

$$\alpha_\parallel = \frac{H^\mathrm{fid}(z) r_{d}^\mathrm{fid}}{H(z) r_{d}}, \;\;\; \alpha_\perp = \frac{D_A(z)\,r_{d}^\mathrm{fid}}{D_A^\mathrm{fid}(z)\,r_{d}}$$

and the isotropic combination $$\alpha_\mathrm{iso} = \alpha_\parallel^{1/3}\alpha_\perp^{2/3}$$.

• Broadband Marginalization: The BAO analysis employs a flexible cubic spline broadband model, keeping the extraction of the oscillatory scale parameter unbiased even in the presence of complex systematics from bias, RSD, and fiber incompleteness (Chen et al., 21 Feb 2024).
• Mock Validation and Error Budget: Large suites of mocks validated each stage of the analysis pipeline; systematic errors from nonlinear bias, template extraction, and modeling choices are individually quantified, yielding a total theoretical+modelling systematics of $\leq0.1\%$ (isotropic) and $\leq0.2\%$ (anisotropic) (Chen et al., 21 Feb 2024).

4. Results and Internal Consistency

DESI’s DR2 BAO measurements reach an unprecedented combined precision of $\sim$0.45% (best composite sample) to 0.52% (six-bin average) across $0.1$z_\mathrm{eff}=2.33$ from $\mathrm{Ly}\alpha$ (Collaboration et al., 18 Mar 2025). The BAO feature is detected with high significance ($>9\,\sigma$ in the optimal redshift bins). Notable results:

• Distance Measurements: Values of $D_M(z)/r_d$ and $D_H(z)/r_d$ are reported in each bin; e.g. (Collaboration et al., 18 Mar 2025):

$$D_H(2.33)/r_d = 8.632\pm0.098_\mathrm{stat}\pm0.026_\mathrm{sys}$$

$$D_M(2.33)/r_d = 38.99\pm0.52_\mathrm{stat}\pm0.12_\mathrm{sys}$$

• Consistency with Previous Surveys: Agreement with BOSS/eBOSS/SDSS is maintained, with careful cross-reanalysis using the DESI pipeline. Variances between footprints (e.g., Legacy Imaging DR9 regions) are consistent with sample variance and photometric systematics (Saulder et al., 18 Jan 2025).
• Low-Redshift Tension: BAO measurements at $z<0.8$ are systematically larger than Planck-2018 $\Lambda$CDM predictions, with a $\sim2.3\sigma$ overall tension in certain cosmological parameters when DESI BAO is combined with Planck (Collaboration et al., 18 Mar 2025).

5. Cosmological Implications: Dark Energy, Hubble Tension, and Neutrino Physics

DESI BAOs, especially when combined with SNe Ia and CMB, profoundly inform cosmological model selection (Collaboration et al., 18 Mar 2025, Collaboration et al., 18 Mar 2025, Collaboration et al., 3 Apr 2024, Jia et al., 4 Jun 2024, Jia et al., 22 Sep 2025):

• Flat $\Lambda$CDM: DESI BAO alone yields $\Omega_\mathrm{m}=0.295\pm0.015$ (Collaboration et al., 3 Apr 2024); the inverse distance ladder (DESI BAO + BBN + $\theta_*$) gives $H_0=68.52\pm0.62$ km s$^{-1}$ Mpc$^{-1}$, consistent with Planck. When combined with Planck full data: $H_0=67.97\pm0.38$ km s$^{-1}$ Mpc$^{-1}$.
• Hints of Dynamical Dark Energy: Allowing $w(z)$ to deviate from $-1$ (CPL parameterization $w=w_0+w_a(1-a)),$ the combination of DESI BAO, CMB, and SNe yields tightest constraints to date, with a mild ($2.6$–$4.2\sigma$) preference for $w_0 > -1$ and $w_a < 0$, suggesting evolving (not constant) dark energy (Collaboration et al., 18 Mar 2025, Collaboration et al., 3 Apr 2024, Jia et al., 22 Sep 2025). Non-parametric reconstructions of $w(z)$ show a downward trend, supporting dynamical dark energy resolution of the $H_0$ tension (Jia et al., 22 Sep 2025).
• Resolution of the Hubble Tension: BAO+SNe-based non-parametric determinations of $w(z)$ and $H_0$ obtain a redshift-dependent $H_0(z)$ which decreases from local values (consistent with Cepheid+SNe) to CMB values at high redshift, naturally resolving the tension as a manifestation of evolving dark energy (Jia et al., 4 Jun 2024, Jia et al., 22 Sep 2025).
• Neutrino Mass and Dark Radiation: Combining DESI BAO with Planck constrains $\sum m_\nu$, e.g., $\sum m_\nu<0.064$ eV (95% CL) in flat $\Lambda$CDM, and 0.16 eV in $w_0w_a$ models (Collaboration et al., 18 Mar 2025). Constraints on $\Delta N_\mathrm{eff}$ relax in dark radiation scenarios (e.g., $\Delta N_\mathrm{eff}\leq 0.39$, a factor $\sim$1.5 weaker than previous SDSS+6dFGS-based limits), especially when allowing late-time dark radiation production (Allali et al., 23 Apr 2024).
• High-Redshift Anchor and Systematics: The inclusion of $\mathrm{Ly}\alpha$ forest BAO at $z>2$ increases redshift lever arm and sharpens dark energy evolution constraints; key systematic terms from non-linear BAO shift ($\sim0.3\%$) are now explicitly included based on simulation studies (Collaboration et al., 18 Mar 2025).

6. Methodological Advances and Systematic Control

The DESI BAO program features several best-practice innovations (Chen et al., 21 Feb 2024, Paillas et al., 3 Apr 2024, Chen et al., 29 Nov 2024):

• Adoption of spline-based broadband marginalization, tested delivery of $\leq 0.1\%$ (isotropic) to $\leq 0.2\%$ (anisotropic) systematic error
• Extensive mock-based pipeline validation, including fiber assignment, mask inhomogeneity, and photometric redshift systematics
• Advanced and robust reconstruction—iterative Fast Fourier Transform (iFFT) or multigrid (MG) solvers—demonstrated to be stable under main parameter choices
• Systematic exploration and quantification of error contributions from nonlinear growth, redshift-space distortions, modeling template extraction, and damping priors

These advances render BAO-derived distances robust against modeling and analysis uncertainties at the level required for percent and sub-percent cosmological precision.

7. Outlook and Future Prospects

With over $14$ million redshifts in DR2 and even greater statistical power anticipated in the full survey, DESI BAOs will further tighten constraints on the cosmic expansion history and thus on the fundamental properties of dark energy, neutrino mass, and new relativistic relics. Further developments will focus on refining Ly$\alpha$ systematic models, quantifying any residual inference bias with even larger simulation suites, and incorporating multi-tracer and cross-correlation analyses (GG, GI, voids, etc.). BAO-based cosmic distances from DESI are poised to serve as the geometric backbone of the next decade’s cosmological model building and for resolving outstanding cosmological anomalies related to the expansion history and new physics in the dark sector.