← Results

Full Shape

Fitting the whole shape of the correlation functions rather than the BAO peak alone. The broadband adds the Alcock-Paczyński effect and the growth rate of structure, at the cost of a model that must describe non-linear scales.

Cosmological constraints combining these measurements with others are collected under Cosmological Parameter Estimation. Forest catalogs, systematics and the pipeline reference set are on the Lyman-α page.

Galaxies & Quasars

Key paper · DR1

DESI 2024 VII: Cosmological Constraints from the Full-Shape Modeling of Clustering Measurements

DESI Collaboration · Journal of Cosmology and Astroparticle Physics 07, 028 (2025) · arXiv:2411.12022

The first DESI full-shape analysis, fitting the two-point clustering of the bright galaxy, luminous red galaxy, emission-line galaxy and quasar samples to constrain the growth of structure and test general relativity.

Supporting papers

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The DR2 full-shape analysis of galaxies and quasars is in preparation.

Lyman-α Forest

Key paper · DR2

DESI DR2 Results IV: Alcock-Paczyński Measurements from the Lyman-α Forest and Cosmological Constraints

DESI Collaboration · arXiv:2607.27410 · 29 July 2026

The Alcock-Paczyński effect measured from the full shape of the DR2 Lyman-α correlation functions rather than the BAO peak alone, constrained to 1% precision at z = 2.33 — twice as tight as the BAO constraint from the same data.

Combining the Lyman-α AP and BAO results gives DH/rd = 8.600 ± 0.066 and DM/rd = 39.32 ± 0.33 — a 6.7-fold reduction in contour area compared with the original DR1 BAO measurement. With a nucleosynthesis prior and assuming ΛCDM, the forest alone yields H0 = 66.5 ± 1.3 km s⁻¹ Mpc⁻¹.

The AP measurement corresponds to Ωm = 0.325 ± 0.018, 1.4σ above DESI BAO, easing the tension with the CMB from 2.4σ to 2.2σ. For a time-evolving dark energy equation of state, DESI and CMB together prefer w0waCDM over ΛCDM at 2.7σ, rising to 3.2σ with supernovae. It is DESI's most precise anchor for the expansion history at z > 1.

Summary drawn from the paper's abstract and Section VI.

Confidence contours in the distance pair D_M/r_d versus D_H/r_d at z = 2.33, showing DESI DR1 BAO in gray, DR2 BAO in blue, DR1 full shape as a dashed purple outline, and the DR2 full-shape result in red, with the Planck ΛCDM prediction in orange and the CMB+BAO w0waCDM prediction outlined in black.
Figure 7. Distance constraints at z = 2.33. The DR2 full-shape result (red) is small enough to begin separating the ΛCDM and w0waCDM predictions.
68% and 95% confidence contours in the dark energy parameters w0 and wa, comparing DESI BAO+CMB as a dashed black outline, DESI BAO plus Lyman-alpha full shape in blue, the same plus CMB in pink, and plus CMB and DES-Dovekie supernovae in green.
Figure 10. Dark energy constraints. Adding the Lyman-α full-shape data shifts the result roughly 0.3σ toward ΛCDM relative to DESI BAO+CMB alone.

Supporting papers · DR2

Released alongside the key paper on 29 July 2026: the validation program completed before unblinding, the mock catalogs it relies on, and the framework connecting one-dimensional and three-dimensional forest clustering.

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DR1

The 2023 Physical Review Letters paper established the method; the DR1 analysis applied it to DESI data.

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