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Baryon Acoustic Oscillations

The 150 Mpc standard ruler — how a sound wave in the primordial plasma became a way to measure distance

The imprint of sound waves in the primordial plasma survives as a preferred separation between galaxies — a standard ruler roughly 150 Mpc long. Measuring it at a range of redshifts maps the expansion history.

DESI measures it two ways: from the clustering of discrete tracers out to z ≈ 2.1, and from Lyman-α forest absorption at z ≈ 2.3. The cosmological constraints drawn from these measurements are collected under Cosmological Parameter Estimation. Forest catalogs, systematics and the pipeline reference set are on the Lyman-α page.

Two panels on a dark background. At left, text reading: size is known; apparent size in sky, about twelve times the diameter of the moon at redshift 1, gives distance, with delta theta from 1.5 to 7 degrees; delta z from 0.04 to 0.13; need good redshift resolution to detect. Below in red: you cannot see BAO rings in the sky, BAO is detected statistically by looking at the whole sky in redshift bins. At right, the simulated distribution today at redshift zero, a broad disk of blue cold dark matter and orange baryon points around a bright central clump, with a white arrow from the center labeled 147 megaparsecs, captioned that the BAO imprint is frozen at about 150 megaparsecs.
In the above figure, blue is cold dark matter and orange is baryons. Dark matter takes no part in the acoustic oscillation: it is pressureless, so the sound wave cannot push it, and it simply stays where it began. Only the baryons are carried outward and left standing in a shell when the wave freezes. The 147 Mpc arrow measures a baryon feature — which is why these are called baryon acoustic oscillations, and why the dark matter shows here as a smooth central concentration rather than a ring.
Why a known length is useful. Because the ruler's true size is fixed by ΛCDM, its apparent size on the sky gives the distance directly — about twelve times the diameter of the moon at z = 1, or Δθ = 1.5°–7° across the survey's redshift range. Along the line of sight the same scale appears as Δz = 0.04–0.13, which sets how good the redshift resolution has to be — and is why DESI is a spectrograph rather than an imager.
The warning in red matters more than it looks. Nothing in the sky is arranged in visible rings. The shell around any one overdensity is a faint statistical excess, swamped by everything else along the line of sight; BAO appears only after correlating millions of galaxies in redshift bins.
By J. W. Rohlf, from Results From DESI, Division of Particles and Fields, Fermilab, July 2026. The simulation is the same one shown running on the ΛCDM page. To get θBAO at a redshift of your choosing, use the Cosmology Calculator with BAO Scale.
Plot of angular BAO scale in degrees against redshift from 0 to 4.3, with a second vertical axis giving comoving distance divided by the sound horizon. A white curve falls steeply from 9 degrees near redshift 0.2 to about 1 degree at redshift 4, following theta equals the sound horizon divided by the comoving distance for fiducial Lambda-CDM. A red dashed horizontal line at 3.2 degrees marks the DESI tile diameter. Colored horizontal bars show the DR2 measurement for each tracer, positioned at its measured angular scale and spanning its redshift range: BGS near 7 degrees, LRG1 near 4.2, LRG2 sitting almost exactly on the 3.2 degree tile line, then L3 plus E1, ELG2, QSO and Lyman alpha all below it, down to about 1.4 degrees. An inset compares the same angular scales as filled circles against a dashed circle representing the 3.2 degree tile, the BGS circle much larger than the tile and the Lyman alpha circle much smaller.
The same angular scale, now measured, and set against the size of a single DESI pointing. The white curve is θBAO = rd/DM(z) for the fiducial cosmology; the bars are the DR2 measurements, each placed at its measured value and spanning its tracer's redshift range.
The red dashed line is the thing to look at. A DESI tile is 3.2° across, and the BAO scale crosses it at around z ≈ 0.7 — right at LRG2. Below that redshift the feature is larger than the field of view, so any patch of sky containing it is built from many separate pointings and the observational systematics of any one tile average down. Above it the feature is smaller than a tile, so a whole BAO-sized patch can sit inside a single pointing — and then whatever that tile does badly is correlated with the signal itself. The inset makes the comparison directly: BGS dwarfs the tile, Lyman-α fits inside it several times over.
By J. W. Rohlf, from Results From DESI, Division of Particles and Fields, Fermilab, July 2026. Bars from DESI DR2, arXiv:2503.14738, Table 4; curve for flat ΛCDM with H0 = 67.36, Ωm = 0.3153, rd = 147.1 Mpc.

Galaxies & Quasars

Key paper · DR2

DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

M. Abdul Karim et al. (DESI Collaboration) · Physical Review D 112, 083515 (2025) · arXiv:2503.14738

BAO from three years of DESI data across the full set of tracers — bright galaxies, luminous red galaxies, emission-line galaxies and quasars.

Key paper · DR1

DESI 2024 III: Baryon Acoustic Oscillations from Galaxies and Quasars

DESI Collaboration · Journal of Cosmology and Astroparticle Physics 04, 012 (2025) · arXiv:2404.03000

The first-year measurement, whose combination with CMB and supernova data first showed a preference for time-evolving dark energy.

Supporting papers

Clustering catalogs and systematics: sample definitions and two-point statistics, BAO reconstruction, fiber-assignment realizations, and halo-occupation systematics for emission-line galaxies.

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Lyman-α Forest

The forest reaches z ≈ 2.3, the only DESI probe deep in the matter-dominated era. Both analyses use the forest auto-correlation together with its cross-correlation with quasar positions.

DR2

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DR1

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Ahead

DESI completed its five-year survey in May 2026. BAO from the full survey is expected in early 2027 and will be added here.