🔭 astrophysics

Probing the matter-dominated expansion with multi-redshift Lyman- $\alpha$ BAO from DESI DR2

This paper presents a multi-redshift Baryon Acoustic Oscillations analysis of DESI DR2 Lyman- $\alpha$ forest data across three redshift bins, achieving high-precision measurements of the expansion history and clustering evolution that are consistent with the $\Lambda$ CDM model and improve curvature constraints when combined with other DESI tracers.

Original authors: Hiram K. Herrera-Alcantar, Julien Guy, Alma X. Gonzalez-Morales, Eric Armengaud, Edwin L. Pérez-Ochoa, Cristhian Garcia-Quintero, J. Aguilar, S. Ahlen, F. Beutler, D. Bianchi, A. Brodzeller, D. Brooks

Published 2026-07-23

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Hiram K. Herrera-Alcantar, Julien Guy, Alma X. Gonzalez-Morales, Eric Armengaud, Edwin L. Pérez-Ochoa, Cristhian Garcia-Quintero, J. Aguilar, S. Ahlen, F. Beutler, D. Bianchi, A. Brodzeller, D. Brooks, E. Chaussidon, T. Claybaugh, A. Cuceu, K. S. Dawson, A. de la Macorra, Arjun Dey, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, G. Gutierrez, C. Hahn, K. Honscheid, D. Huterer, M. Ishak, T. Karim, R. Kehoe, D. Kirkby, A. Kremin, O. Lahav, A. Lambert, M. Landriau, L. Le Guillou, M. Manera, P. Martini, A. Meisner, R. Miquel, J. Moustakas, A. Muñoz-Gutiérrez, S. Nadathur, G. Niz, E. Paillas, N. Palanque-Delabrouille, W. J. Percival, C. Poppett, F. Prada, I. Pérez-Ràfols, C. Ravoux, G. Rossi, R. Ruggeri, L. Samushia, E. Sanchez, C. Saulder, D. Schlegel, M. Schubnell, H. Seo, J. Silber, G. Tarlé, B. A. Weaver, C. Yèche, 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 loaf of raisin bread. As the dough rises, the raisins (galaxies) move away from each other, not because they are swimming through the dough, but because the dough itself is stretching. For decades, astronomers have been trying to measure exactly how fast this dough is rising at different times in history. To do this, they look for "fossil footprints" left over from the very beginning of time: the Baryon Acoustic Oscillations (BAO). Think of these as a standard ruler, a cosmic yardstick imprinted in the distribution of matter that has remained the same size since the universe was a baby. By measuring how big this ruler looks to us today at different distances, we can figure out how much the universe has stretched since that light left its source.

The big mystery this paper tackles is what happened during the "teenage years" of the universe, roughly 10 to 11 billion years ago. During this era, the universe was dominated by matter (stuff like atoms and dark matter) rather than the mysterious dark energy that is speeding up the expansion today. The standard theory, called the Einstein-de Sitter model, predicts a very specific way the universe should expand during this time, like a car coasting with a specific amount of friction. If the expansion rate doesn't match this prediction, it would mean our understanding of gravity or the ingredients of the universe is wrong. The challenge is that looking back this far is like trying to read a book through a thick, foggy window; the light is faint, and the "fog" (the intergalactic gas) is messy.

This paper, led by a team using the Dark Energy Spectroscopic Instrument (DESI), decides to clear up that fog by looking at the universe in three distinct time slices instead of one big blur. They analyzed the light from over a million quasars (super-bright beacons powered by black holes) and the "Lyman-alpha forest"—a pattern of shadows in the quasar light caused by clouds of hydrogen gas between us and the quasars. By splitting these shadows into three groups based on how far away they are (redshifts of roughly 2.13, 2.40, and 2.81), the team created a high-resolution movie of the universe's expansion during its matter-dominated era.

The results are a strong confirmation of our current cosmic recipe. The team measured the expansion rate at these three different times and found that it follows the expected pattern for a universe dominated by matter. Specifically, they found that the expansion rate scales with redshift in a way that matches the standard model with a precision of about 12%. While the data leans slightly toward the predictions of the standard "Lambda Cold Dark Matter" (ΛCDM) model rather than a perfectly simple matter-only model, the difference is not statistically significant enough to rule out the simple model yet. Essentially, the universe is behaving exactly as the textbooks say it should during this era.

Beyond just measuring the expansion, the paper also acts like a cosmic detective, tracking how the "clumpiness" of the universe changes over time. They measured how the gas clouds and the quasars themselves cluster together as the universe ages. They found that the gas clouds become more "biased" (more likely to cluster in specific spots) as we look further back in time, while the quasars follow a predictable growth pattern that matches independent measurements. This consistency is a huge win; it means the tools we use to measure the universe are working correctly and that our understanding of how matter clumps together is solid.

The team also checked their work rigorously, using thousands of computer simulations to ensure their methods weren't tricking them. They found that their measurements are robust and that the "noise" in the data (like small errors in measuring the distance to quasars) doesn't significantly skew the final result. When they combined their new three-slice measurements with other data from galaxies and supernovae, the results tightened the constraints on the shape of the universe, suggesting it is flat (like a sheet of paper) with even greater confidence than before.

In short, this paper doesn't overturn the laws of physics, but it does a fantastic job of verifying them in a difficult-to-reach corner of the cosmos. It confirms that the universe's expansion history during its matter-dominated phase is consistent with our best theories, providing a solid foundation for future searches for new physics. The "fog" of the early universe has been pierced just enough to see that the cosmic ruler is holding steady, and the universe is expanding exactly as the Friedmann equations predicted.

Technical Summary: Probing the matter-dominated expansion with multi-redshift Lyman-α BAO from DESI DR2

Problem and Motivation
The Dark Energy Spectroscopic Instrument (DESI) has produced the most precise large-scale structure Baryon Acoustic Oscillation (BAO) measurements at redshifts $z > 2$ to date, utilizing the Lyman- $\alpha$ (Ly $\alpha$ ) forest. Previous DESI analyses (DR1 and DR2) compressed the Ly $\alpha$ forest information into a single effective redshift ( $z_{\rm eff} = 2.33$ ). While this approach yielded high-precision distance measurements, it averaged over the strong redshift evolution of the Ly $\alpha$ forest bias and other astrophysical parameters. Furthermore, a single-bin analysis precludes a direct, cosmology-independent test of the expansion history within the matter-dominated era ( $2 \lesssim z \lesssim 3$ ), where dark energy is dynamically subdominant. This paper addresses the need to resolve the evolution of BAO distance scales and astrophysical parameters across cosmic time by splitting the DESI DR2 Ly $\alpha$ sample into multiple redshift bins.

Methodology
The authors re-analyze the DESI DR2 Ly $\alpha$ forest data (over 820,000 quasar spectra and 1.2 million quasar positions) using a novel pair-based redshift binning scheme. Unlike previous forest-level binning (e.g., in eBOSS), this method assigns individual pixel-pixel and pixel-quasar pairs to redshift bins based on their mean pair redshift, $z_{\rm pair}$ . The sample is divided into three bins: $z_{\rm pair} \le 2.25$ , $2.25 < z_{\rm pair} \le 2.6$ , and $z_{\rm pair} > 2.6$ , corresponding to effective redshifts $z_{\rm eff} = 2.13, 2.40,$ and $2.81$.

Key methodological adaptations include:

Correlation Function Estimation: Computing auto-correlations (Ly $\alpha \times$ Ly $\alpha$ ) and cross-correlations (Ly $\alpha \times$ QSO) within these specific pair-level bins.
Distortion Matrix: Adapting the distortion matrix to account for the fact that a single forest can contribute to multiple bins, potentially inducing cross-bin correlations due to continuum-fitting distortions. The authors quantify these cross-bin correlations in Appendix A, finding them negligible at current precision.
Modeling: Fitting the correlation functions using the standard DESI DR2 Ly $\alpha$ BAO model (implemented in the Vega package), which includes BAO scale parameters ( $\alpha_\parallel, \alpha_\perp$ ), nuisance parameters for metal contamination, high-column density (HCD) systems, quasar redshift errors, and the transverse proximity effect.
Validation: The pipeline is validated on 400 synthetic datasets (300 CoLoRe-QL and 100 Saclay mocks). The analysis confirms unbiased recovery of BAO parameters and well-calibrated uncertainties, though it identifies a systematic shift in $\chi^2$ distributions caused by covariance matrix smoothing, which affects goodness-of-fit statistics but not parameter estimates.

Key Results

BAO Measurements: The analysis yields isotropic BAO measurements with $\sim 1.1\text{--}1.2\%$ precision per bin. The derived distance ratios show a clear evolution:
- The isotropic dilation parameter $D_V/r_d$ increases from $30.26 \pm 0.39$ to $32.22 \pm 0.47$ .
- The Alcock-Paczyński parameter $D_M/D_H$ increases from $3.96 \pm 0.15$ to $5.63^{+0.22}_{-0.24}$ .
- The Hubble distance $D_H/r_d$ decreases from $9.40 \pm 0.20$ to $7.22 \pm 0.17$ .
- The lowest redshift bin ( $z_{\rm eff}=2.13$ ) exhibits a low probability to exceed (PTE = 0.01), attributed to localized small-scale systematics and covariance smoothing, but the recovered BAO scale remains robust under various tests.
Redshift Evolution of Parameters: The multi-bin fit provides a self-consistent measurement of parameter evolution:
- Ly $\alpha$ Bias: Evolves as $(1+z)^{\gamma_\alpha}$ with $\gamma_\alpha = 3.05 \pm 0.16$ , consistent with the standard scaling of $\sim 2.9$ .
- RSD Parameter: The effective RSD parameter $\beta'_\alpha$ decreases with redshift, with an evolution index $\gamma_\beta = -0.97 \pm 0.26$ , showing a $\sim 3.7\sigma$ preference for non-zero evolution.
- Quasar Bias: Evolves as $(1+z)^{\gamma_Q}$ with $\gamma_Q = 1.56 \pm 0.23$ , consistent with independent quasar clustering measurements.
Expansion History Test: Using the radial distance measurements ( $D_H/r_d$ ), the authors perform a direct test of the matter-dominated expansion history. Fitting the model $H(z) \propto (1+z)^n$ yields $n = 1.34 \pm 0.16$ . This result is consistent with the Einstein-de Sitter expectation ( $n=1.5$ ) at the $1\sigma$ level and represents a first direct, $\sim 12\%$ precision test of the Friedmann equations in this redshift regime. Synthetic data generated from the fiducial $\Lambda$ CDM cosmology yields $n = 1.42 \pm 0.16$ , suggesting the data slightly favors the $\Lambda$ CDM prediction over pure Einstein-de Sitter, though current uncertainties prevent a definitive distinction.
Cosmological Constraints: When combined with other DESI DR2 tracers (galaxies and quasars) and external datasets (CMB and supernovae):
- Constraints on flat $\Lambda$ CDM and $w_0w_a$ CDM models remain consistent with single-bin analyses, with negligible shifts in parameter means.
- For the non-flat model ( $\Lambda$ CDM + $\Omega_K$ ), the three-bin analysis improves the Figure of Merit by $\sim 15\%$ in the $(\Omega_m, \Omega_K)$ plane, tightening the curvature constraint from $10^3\Omega_K = 25 \pm 41$ (single-bin) to $10^3\Omega_K = -5 \pm 36$ .

Significance
The paper claims to present the first multi-redshift Ly $\alpha$ BAO analysis using DESI data. Its primary significance lies in demonstrating the feasibility of splitting the Ly $\alpha$ forest sample to simultaneously measure BAO distances and the redshift evolution of astrophysical biases within a single framework. This approach enables a direct, model-independent probe of the expansion history during the matter-dominated era, a regime previously inaccessible to galaxy surveys. The results validate the robustness of the DESI Ly $\alpha$ pipeline against redshift-dependent systematics and provide a foundation for future analyses (e.g., DESI Run 2, Spec-S5) that will leverage higher statistics and extended redshift ranges to further refine measurements of the expansion history and dark energy properties.

More like this