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DESI DR2 Results IV: Alcock-Paczynski Measurements from the Lyman Alpha Forest and Cosmological Constraints

Using the second data release of the Dark Energy Spectroscopic Instrument (DESI), this paper presents precise Alcock-Paczyński measurements from the Lyman- $\alpha$ forest that constrain the expansion history at $z \approx 2.33$ , yielding a Hubble constant of $66.5 \pm 1.3$ km/s/Mpc and providing stronger evidence for a time-evolving dark energy equation of state when combined with CMB and supernova data.

Original authors: DESI Collaboration, A. G. Adame, J. Aguilar, S. Ahlen, O. Alves, A. Anand, U. Andrade, E. Armengaud, S. Avila, A. Aviles, P. Bansal, A. Bault, J. R. Bermejo-Climent, F. Beutler, D. Bianchi, C. BlakeDESI Collaboration, A. G. Adame, J. Aguilar, S. Ahlen, O. Alves, A. Anand, U. Andrade, E. Armengaud, S. Avila, A. Aviles, P. Bansal, A. Bault, J. R. Bermejo-Climent, F. Beutler, D. Bianchi, C. Blake, S. Blasby, M. Bonici, S. Brieden, A. Brodzeller, D. Brooks, A. Carnero Rosell, K. Carrion, L. Casas, F. J. Castander, E. Chaussidon, J. Chaves-Montero, D. Chebat, X. Chen, Z. Chen, Y. Cho, T. Claybaugh, A. Cuceu, T. M. Davis, K. S. Dawson, R. de Belsunce, A. de la Macorra, J. Della Costa, A. Dey, M. Doshi, H. Ebina, D. J. Eisenstein, W. Elbers, G. Farren, V. A. Fawcett, E. Fernández-García, S. Ferraro, A. Font-Ribera, D. Forero-Sánchez, J. E. Forero-Romero, C. S. Frenk, G. Gambardella, C. Garcia-Quintero, L. H. Garrison, H. Gil-Marín, S. Gontcho A Gontcho, A. X. Gonzalez-Morales, C. Gordon, D. Green, R. Gsponer, G. Gutierrez, J. Guy, B. Hadzhiyska, C. Hahn, S. He, M. Herbold, H. K. Herrera-Alcantar, M. -F. Ho, K. Honscheid, J. Hou, D. Huterer, V. Iršič, M. Ishak, J. -Q. Jiang, S. Jos, S. Juneau, N. V. Kamble, N. G. Karaçaylı, T. Karim, D. Kirkby, A. Kremin, A. Krolewski, O. Lahav, C. Lamman, M. Landriau, J. Lasker, J. M. Le Goff, L. Le Guillou, A. Leauthaud, Q. Li, W. Liu, K. Lodha, Y. Luo, O. Manasoiu, M. Manera, P. Martini, M. Maus, A. Meisner, R. Miquel, J. Morawetz, J. Moustakas, E. Mueller, P. Mukherjee, A. Muñoz-Gutiérrez, A. D. Myers, S. Nadathur, J. Najita, G. Niz, H. E. Noriega, E. Paillas, N. Palanque-Delabrouille, J. Pan, M. P. Ibanez, W. J. Percival, A. Porredon, F. Prada, H. Pulido-Hernández, A. Pérez-Fernández, I. Pérez-Ràfols, A. Raichoor, M. Rashkovetskyi, J. Ratajczak, C. Ravoux, A. Robertson, A. Rocher, J. Rohlf, A. J. Ross, G. Rossi, R. Ruggeri, M. F. Ruiz-Herrera Bernal, L. Samushia, E. Sanchez, C. Saulder, D. Schlegel, H. Seo, A. Shafieloo, R. Sharples, J. Silber, F. Sinigaglia, M. Siudek, T. Tan, G. Tarlé, W. Turner, R. Vaisakh, M. Vargas-Magaña, B. A. Weaver, M. Wolfson, H. Yang, J. Yu, C. Yèche, H. Zhang, Y. Zhang, R. Zhao, R. Zhou

Published 2026-07-31

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CC BY 4.0

Original authors: DESI Collaboration, A. G. Adame, J. Aguilar, S. Ahlen, O. Alves, A. Anand, U. Andrade, E. Armengaud, S. Avila, A. Aviles, P. Bansal, A. Bault, J. R. Bermejo-Climent, F. Beutler, D. Bianchi, C. Blake, S. Blasby, M. Bonici, S. Brieden, A. Brodzeller, D. Brooks, A. Carnero Rosell, K. Carrion, L. Casas, F. J. Castander, E. Chaussidon, J. Chaves-Montero, D. Chebat, X. Chen, Z. Chen, Y. Cho, T. Claybaugh, A. Cuceu, T. M. Davis, K. S. Dawson, R. de Belsunce, A. de la Macorra, J. Della Costa, A. Dey, M. Doshi, H. Ebina, D. J. Eisenstein, W. Elbers, G. Farren, V. A. Fawcett, E. Fernández-García, S. Ferraro, A. Font-Ribera, D. Forero-Sánchez, J. E. Forero-Romero, C. S. Frenk, G. Gambardella, C. Garcia-Quintero, L. H. Garrison, H. Gil-Marín, S. Gontcho A Gontcho, A. X. Gonzalez-Morales, C. Gordon, D. Green, R. Gsponer, G. Gutierrez, J. Guy, B. Hadzhiyska, C. Hahn, S. He, M. Herbold, H. K. Herrera-Alcantar, M. -F. Ho, K. Honscheid, J. Hou, D. Huterer, V. Iršič, M. Ishak, J. -Q. Jiang, S. Jos, S. Juneau, N. V. Kamble, N. G. Karaçaylı, T. Karim, D. Kirkby, A. Kremin, A. Krolewski, O. Lahav, C. Lamman, M. Landriau, J. Lasker, J. M. Le Goff, L. Le Guillou, A. Leauthaud, Q. Li, W. Liu, K. Lodha, Y. Luo, O. Manasoiu, M. Manera, P. Martini, M. Maus, A. Meisner, R. Miquel, J. Morawetz, J. Moustakas, E. Mueller, P. Mukherjee, A. Muñoz-Gutiérrez, A. D. Myers, S. Nadathur, J. Najita, G. Niz, H. E. Noriega, E. Paillas, N. Palanque-Delabrouille, J. Pan, M. P. Ibanez, W. J. Percival, A. Porredon, F. Prada, H. Pulido-Hernández, A. Pérez-Fernández, I. Pérez-Ràfols, A. Raichoor, M. Rashkovetskyi, J. Ratajczak, C. Ravoux, A. Robertson, A. Rocher, J. Rohlf, A. J. Ross, G. Rossi, R. Ruggeri, M. F. Ruiz-Herrera Bernal, L. Samushia, E. Sanchez, C. Saulder, D. Schlegel, H. Seo, A. Shafieloo, R. Sharples, J. Silber, F. Sinigaglia, M. Siudek, T. Tan, G. Tarlé, W. Turner, R. Vaisakh, M. Vargas-Magaña, B. A. Weaver, M. Wolfson, H. Yang, J. Yu, C. Yèche, H. Zhang, Y. Zhang, R. Zhao, R. Zhou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, expanding balloon. For decades, scientists have been trying to figure out exactly how fast that balloon is inflating and what invisible force is pushing it to expand faster and faster. This invisible pusher is called "dark energy," and understanding it is one of the biggest mysteries in modern science. To measure the expansion, astronomers use "standard rulers"—specific patterns in the distribution of galaxies and gas that act like a known length of tape measure stretched across the cosmos. By seeing how big or small these rulers look from Earth at different times in the universe's history, scientists can calculate how much the universe has stretched. The big question is: Is the universe expanding at a steady, predictable pace, or is the dark energy pushing it changing its mind over time?

This new paper from the Dark Energy Spectroscopic Instrument (DESI) collaboration dives deep into the "Lyman-alpha forest," which is a bit like a cosmic barcode. When light from distant, ancient quasars (super-bright black holes) travels through space to reach us, it passes through clouds of hydrogen gas. These clouds absorb specific colors of light, leaving a jagged pattern of dark lines in the spectrum, much like a barcode. Because this gas is everywhere, the "forest" of lines gives us a 3D map of the universe when it was young and mostly made of matter, rather than dark energy. The paper focuses on a specific trick called the Alcock-Paczyński (AP) effect. Imagine looking at a perfectly round beach ball through a funhouse mirror that stretches it vertically but squishes it horizontally. If you know the ball is supposed to be round, you can tell exactly how the mirror is distorting it. Similarly, if the universe is supposed to be isotropic (looking the same in all directions), any distortion in the shape of the cosmic "beach balls" (galaxy clusters and gas clouds) tells us how the universe is expanding.

The authors of this paper used the second data release (DR2) from DESI, which includes over 820,000 spectra of the Lyman-alpha forest and positions of over 1.2 million quasars. They didn't just look for the "standard ruler" (the Baryon Acoustic Oscillation, or BAO) to measure distances; they looked at the entire shape of the cosmic barcode. By analyzing the full pattern of the forest, they were able to measure the AP effect with incredible precision. They found that at an effective redshift of $z_{eff} = 2.33$ (a time when the universe was about one-third of its current age), they could constrain the ratio of two cosmic distances, $D_M/D_H$ , to within 1% precision. This is twice as precise as their previous measurements using only the standard ruler from the same data.

When they combined this new, super-precise measurement with other data, they found some interesting things. First, the results fit very well with the standard model of cosmology, known as $\Lambda$ CDM, which assumes dark energy is a constant force. However, they also tested models where dark energy changes over time (called $w_0w_a$ CDM). While the standard model still fits the data well, the combination of DESI data with Cosmic Microwave Background (CMB) data showed a slight preference for a changing dark energy, though the new Lyman-alpha measurement actually pulled the results slightly closer to the standard constant model, reducing the tension between different datasets from $2.4\sigma$ to $2.2\sigma$ .

The paper also calculated the Hubble constant ( $H_0$ ), which describes the current expansion rate of the universe, using only high-redshift data and a prior on the density of ordinary matter from Big Bang Nucleosynthesis. They found $H_0 = 66.5 \pm 1.3 \text{ km s}^{-1} \text{ Mpc}^{-1}$ . This value is consistent with measurements from the early universe but sits in tension with measurements from the "local" universe (nearby galaxies), a discrepancy known as the Hubble Tension. Additionally, they set new limits on the sum of neutrino masses, finding an upper bound of $\sum m_\nu < 0.0592 \text{ eV}$ (95% confidence) when combining their data with CMB observations, which is very close to the minimum mass required by particle physics experiments.

In short, this paper doesn't prove that dark energy is changing, nor does it solve the Hubble Tension. Instead, it provides the most precise "anchor" yet for how the universe expanded when it was young and matter-dominated. By using the full shape of the Lyman-alpha forest rather than just a single ruler, they tightened the constraints on cosmic distances by a factor of two compared to previous methods. The results suggest that while the standard model of a constant dark energy is still the best fit, the data is now precise enough to start distinguishing between different theories of dark energy, and future data releases will likely sharpen this picture even further.

Technical Summary: DESI DR2 Results IV: Alcock–Paczyński Measurements from the Lyman Alpha Forest and Cosmological Constraints

Problem and Motivation
The physics of cosmic acceleration remains a primary challenge in cosmology, requiring increasingly precise constraints on the expansion rate across a wide redshift range. While Baryon Acoustic Oscillations (BAO) have long served as a standard ruler, recent measurements from the Dark Energy Spectroscopic Instrument (DESI) suggest that dark energy may not be a simple cosmological constant. To improve constraints on the expansion history at redshifts $z > 2$ , where large galaxy surveys have historically struggled, this paper utilizes the full shape of Lyman- $\alpha$ (Ly $\alpha$ ) forest correlation functions. Unlike traditional BAO analyses that focus solely on the acoustic peak, this work leverages the Alcock–Paczyński (AP) effect present across all scales in the Ly $\alpha$ forest to tighten constraints on the cosmic expansion rate.

Methodology
The analysis utilizes the second data release (DR2) from DESI, comprising over 820,000 Ly $\alpha$ forest spectra and positions of over 1.2 million quasars. The dataset represents a doubling of the sample size compared to the first data release (DR1), with improved signal-to-noise ratios due to multiple observations of many quasars.

The methodology involves measuring four correlation functions: Ly $\alpha$ (A) $\times$ Ly $\alpha$ (A), Ly $\alpha$ (A) $\times$ Ly $\alpha$ (B), Ly $\alpha$ (A) $\times$ QSO, and Ly $\alpha$ (B) $\times$ QSO. The analysis employs a template-based approach that separates the correlation function into a "peak" (BAO) component and a "smooth" (broadband) component.

AP Parametrization: The AP effect is isolated using a parameter $\phi \equiv q_\perp / q_\parallel$ , which measures the ratio of the true transverse to Hubble distance ( $D_M/D_H$ ) relative to a fiducial cosmology. The analysis measures $\phi$ for both the BAO peak ( $\phi_p$ ) and the broadband smooth component ( $\phi_s$ ).
Modeling and Marginalization: The model accounts for redshift-space distortions (RSD), quasar redshift errors, high column density (HCD) absorbers, metal contamination, and UV background fluctuations. A key methodological advancement is a new small-scale marginalization framework. This addresses distortions introduced by continuum fitting, which mix information from small scales ( $r < r_{min}$ ) into larger scales. By analytically marginalizing over linear templates in the undistorted model space, the analysis effectively removes sensitivity to non-linear small-scale physics without discarding data.
Validation: The analysis was validated using two types of mock catalogs: AbacusSummit N-body simulations and new CoLoRe 2LPT light-cone mocks. Additionally, extensive blinded robustness tests were performed, including data splits (e.g., by signal-to-noise ratio) and variations in analysis choices (e.g., priors, scale cuts). The baseline analysis was selected based on these blinded tests to ensure unbiased results within a tolerance of $1/3$ of the statistical uncertainty.

Key Contributions

First Full-Shape AP Measurement from DESI DR2: The paper presents the first measurement of the AP effect using the full shape of Ly $\alpha$ forest correlations from DESI DR2, isolating the broadband signal ( $\phi_s$ ) distinct from the BAO peak.
Methodological Improvements: The introduction of a formalism for small-scale marginalization allows for the inclusion of data down to smaller scales while mitigating biases from continuum fitting distortions. Additionally, the model incorporates a scale-dependent Ly $\alpha$ bias driven by UV background fluctuations, which was detected at high significance ( $\sim 3\sigma$ to $5\sigma$ ).
Updated Systematic Error Budget: Based on mock validation, the paper updates the systematic error budget for BAO measurements, specifically increasing the uncertainty in the AP direction ( $\Delta \phi_p = 0.8\%$ ) to account for non-linear evolution shifts observed in mocks.

Results

AP Constraints: The broadband AP measurement yields a constraint on the distance ratio $D_M/D_H$ at an effective redshift $z_{eff} = 2.33$ with 1% precision ( $\phi_s = 1.007 \pm 0.011$ ). This is twice as tight as the BAO-only constraint from the same dataset and represents a $\sim 45\%$ improvement over the DR1 full-shape analysis.
Cosmological Distances: Combining the broadband AP and BAO results, the paper measures:
- $D_H(z_{eff})/r_d = 8.600 \pm 0.066$ (0.8% precision)
- $D_M(z_{eff})/r_d = 39.32 \pm 0.33$ (0.8% precision)
  These constraints exceed the original 5-year DESI survey requirements using only the first three years of data.
$\Lambda$ CDM Constraints: Within the flat $\Lambda$ CDM model, the Ly $\alpha$ forest alone constrains the matter fraction to $\Omega_m = 0.325 \pm 0.018$ . When combined with DESI BAO (galaxy and quasar clustering), the joint constraint is $\Omega_m = 0.3012 \pm 0.0079$ .
Hubble Constant: Using the Ly $\alpha$ result combined with a Big Bang Nucleosynthesis (BBN) prior on baryon density, the paper derives a Hubble constant of $H_0 = 66.5 \pm 1.3$ km s $^{-1}$ Mpc $^{-1}$ , independent of CMB anisotropies.
Tension with CMB: The inclusion of the new Ly $\alpha$ AP measurement shifts the DESI results slightly toward the CMB prediction, reducing the tension between DESI and the Planck CMB from $2.4\sigma$ to $2.2\sigma$ .
Extended Models:
- Dark Energy: In the $w_0w_a$ CDM model, the preference for evolving dark energy over $\Lambda$ CDM is reduced when including the new Ly $\alpha$ data. For the DESI+CMB combination, the preference drops from $3.2\sigma$ to $2.7\sigma$ .
- Neutrino Masses: The upper limit on the sum of neutrino masses is relaxed slightly to $\sum m_\nu < 0.0592$ eV (95% CL) in $\Lambda$ CDM when including Ly $\alpha$ data, due to the preference for a slightly higher $\Omega_m$ .
- Curvature: The results are consistent with a flat universe, with a mild statistical preference ( $\sim 2\sigma$ ) for an open universe in the DESI+CMB combination.

Significance
The paper claims that the new Ly $\alpha$ AP measurement provides DESI's most precise anchor for the expansion history at $z > 1$ in the matter-dominated universe. By achieving 1% precision on the AP effect, the analysis allows for the first time a meaningful separation between $\Lambda$ CDM and dynamical dark energy models ( $w_0w_a$ CDM) using Ly $\alpha$ forest data alone. The results demonstrate that the Ly $\alpha$ forest is a robust probe for high-redshift cosmology, capable of tightening constraints on the expansion rate and testing extensions to the standard model with unprecedented precision. The authors emphasize that these results are robust against systematic uncertainties, validated through rigorous mock and blinded data tests, and represent a significant step forward in understanding cosmic acceleration.

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