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Full Shape

Fitting the whole correlation function, not just the BAO peak — the Alcock-Paczyński effect and the growth rate

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-\(\alpha\) 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-\(\alpha\) Forest

Key paper · DR2

DESI DR2 Results IV: Alcock-Paczyński Measurements from the Lyman-\(\alpha\) 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-\(\alpha\) 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-\(\alpha\) AP and BAO results gives \(D_\mathrm{H}/r_\mathrm{d} = 8.600 \pm 0.066\) and \(D_\mathrm{M}/r_\mathrm{d} = 39.32 \pm 0.33\) — a 6.7-fold reduction in contour area compared with the original DR1 BAO measurement. With a nucleosynthesis prior and assuming \(\Lambda\)CDM, the forest alone yields \(H_0 = 66.5 \pm 1.3\ \mathrm{km\,s^{-1}\,Mpc^{-1}}\).

The AP measurement corresponds to \(\Omega_\mathrm{m} = 0.325 \pm 0.018\), \(1.4\sigma\) above DESI BAO, easing the tension with the CMB from \(2.4\sigma\) to \(2.2\sigma\). For a time-evolving dark energy equation of state, DESI and CMB together prefer \(w_0w_a\)CDM over \(\Lambda\)CDM at \(2.7\sigma\), rising to \(3.2\sigma\) 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 \(\Lambda\)CDM and \(w_0w_a\)CDM 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-\(\alpha\) full-shape data shifts the result roughly \(0.3\sigma\) toward \(\Lambda\)CDM relative to DESI BAO+CMB alone. The evolving dark energy calculator lets you move around this plane and read off what each \(w_0, w_a\) implies.

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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