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We perform an analysis of the full shapes of Lyman-αα (Lyαα) forest correlation functions measured from the first data release (DR1) of the Dark Energy Spectroscopic Instrument (DESI). Our analysis focuses on measuring the Alcock-Paczynski (AP) effect and the cosmic growth rate times the amplitude of matter fluctuations in spheres of 88h−1Mpch−1Mpc, fσ8fσ8​. We validate our measurements using two different sets of mocks, a series of data splits, and a large set of analysis variations, which were first performed blinded. Our analysis constrains the ratio DM/DH(zeff)=4.525±0.071DM​/DH​(zeff​)=4.525±0.071, where DH=c/H(z)DH​=c/H(z) is the Hubble distance, DMDM​ is the transverse comoving distance, and the effective redshift is zeff=2.33zeff​=2.33. This is a factor of 2.42.4 tighter than the Baryon Acoustic Oscillation (BAO) constraint from the same data. When combining with Lyαα BAO constraints from DESI DR2, we obtain the ratios DH(zeff)/rd=8.646±0.077DH​(zeff​)/rd​=8.646±0.077 and DM(zeff)/rd=38.90±0.38DM​(zeff​)/rd​=38.90±0.38, where rdrd​ is the sound horizon at the drag epoch. We also measure fσ8(zeff)=0.37  −0.065+0.055 (stat) ±0.033 (sys)fσ8​(zeff​)=0.37−0.065+0.055​(stat)±0.033(sys), but we do not use it for cosmological inference due to difficulties in its validation with mocks. In ΛΛCDM, our measurements are consistent with both cosmic microwave background (CMB) and galaxy clustering constraints. Using a nucleosynthesis prior but no CMB anisotropy information, we measure the Hubble constant to be H0=68.3±1.6   km s−1 Mpc−1H0​=68.3±1.6kms−1Mpc−1 within ΛΛCDM. Finally, we show that Lyαα forest AP measurements can help improve constraints on the dark energy equation of state, and are expected to play an important role in upcoming DESI analyses.

In preparation for the first cosmological measurements from the full-shape of the Lyman- (Ly ) forest from DESI, we must carefully model all relevant systematics that might bias our analysis. It was shown in Youles et al. (2022) that random quasar redshift errors produce a smoothing effect on the mean quasar continuum in the Ly forest region. This in turn gives rise to spurious features in the Ly auto-correlation, and its cross-correlation with quasars. Using synthetic data sets based on the DESI survey, we confirm that the impact on BAO measurements is small, but that a bias is introduced to parameters which depend on the full-shape of our correlations. We combine a model of this contamination in the cross-correlation (Youles et al. 2022) with a new model we introduce here for the auto-correlation. These are parametrised by 3 parameters, which when included in a joint fit to both correlation functions, successfully eliminate any impact of redshift errors on our full-shape constraints. We also present a strategy for removing this contamination from real data, by removing 0.3% of correlating pairs.

Correlations in the Lyman- (Ly ) forest, both as a function of line of sight separation (1D) and 3D separation, provide a unique window to the distribution of matter at redshifts not accessible by current galaxy surveys. While optimal quadratic estimators have been used to measure 1D correlations, they are computationally expensive and difficult to extend to 3D analyses. On the other hand, estimators based on the Fast Fourier Transform (FFT) are significantly faster, but are affected by missing data in the spectra (masked pixels) and so far have not used pixel weights to reduce the uncertainties in the measurement. In this publication we describe how to compute the window matrix that enables forward-modeling the impact of masked pixels and weights on the FFT-based estimators. We use Gaussian and hydrodynamical simulations with artificially masked pixels to validate the method on the measurement of 1D correlations. Finally, we show that the formalism can be extended to model the impact on 3D correlations, in particular on the cross-spectrum, the correlation of 1D Fourier modes as a function of transverse separation. This work will enable more precise clustering measurements with the Ly forest dataset recently collected by the Dark Energy Spectroscopic Instrument (DESI).

We present the Baryon Acoustic Oscillation (BAO) measurements with the Lyman-alpha (LyA) forest from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI) survey. Our BAO measurements include both the auto-correlation of the LyA forest absorption observed in the spectra of high-redshift quasars and the cross-correlation of the absorption with the quasar positions. The total sample size is approximately a factor of two larger than the DR1 dataset, with forest measurements in over 820,000 quasar spectra and the positions of over 1.2 million quasars. We describe several significant improvements to our analysis in this paper, and two supporting papers describe improvements to the synthetic datasets that we use for validation and how we identify damped LyA absorbers. Our main result is that we have measured the BAO scale with a statistical precision of 1.1% along and 1.3% transverse to the line of sight, for a combined precision of 0.65% on the isotropic BAO scale at zeff=2.33zeff​=2.33. This excellent precision, combined with recent theoretical studies of the BAO shift due to nonlinear growth, motivated us to include a systematic error term in LyA BAO analysis for the first time. We measure the ratios DH(zeff)/rd=8.632±0.098±0.026DH​(zeff​)/rd​=8.632±0.098±0.026 and DM(zeff)/rd=38.99±0.52±0.12DM​(zeff​)/rd​=38.99±0.52±0.12, where DH=c/H(z)DH​=c/H(z) is the Hubble distance, DMDM​ is the transverse comoving distance, rdrd​ is the sound horizon at the drag epoch, and we quote both the statistical and the theoretical systematic uncertainty. The companion paper presents the BAO measurements at lower redshifts from the same dataset and the cosmological interpretation.

The second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI), containing data from the first three years of observations, doubles the number of Lyman-αα (Lyαα) forest spectra in DR1 and it provides the largest dataset of its kind. To ensure a robust validation of the Baryonic Acoustic Oscillation (BAO) analysis using Lyαα forests, we have made significant updates compared to DR1 to both the mocks and the analysis framework used in the validation. In particular, we present CoLoRe-QL, a new set of Lyαα mocks that use a quasi-linear input power spectrum to incorporate the non-linear broadening of the BAO peak. We have also increased the number of realisations used in the validation to 400, compared to the 150 realisations used in DR1. Finally, we present a detailed study of the impact of quasar redshift errors on the BAO measurement, and we compare different strategies to mask Damped Lyman-αα Absorbers (DLAs) in our spectra. The BAO measurement from the Lyαα dataset of DESI DR2 is presented in a companion publication.

On large scales, measurements of the Lyman-α forest offer insights into the expansion history of the Universe, while on small scales, these impose strict constraints on the growth history, the nature of dark matter, and the sum of neutrino masses. This work introduces ForestFlow, a cosmological emulator designed to bridge the gap between large- and small-scale Lyman-α forest analyses. Using conditional normalizing flows, ForestFlow emulates the 2 Lyman-α linear biases (bδ and bη) and 6 parameters describing small-scale deviations of the 3D flux power spectrum (P3D) from linear theory. These 8 parameters are modeled as a function of cosmology – the small-scale amplitude and slope of the linear power spectrum – and the physics of the intergalactic medium. Thus, in combination with a Boltzmann solver, ForestFlow can predict P3D on arbitrarily large (linear) scales and the 1D flux power spectrum (P1D) – the primary observable for small-scale analyses – without the need for interpolation or extrapolation. Consequently, ForestFlow enables for the first time multiscale analyses. Trained on a suite of 30 fixed-and-paired cosmological hydrodynamical simulations spanning redshifts from z=2 to 4.5, ForestFlow achieves 3 and 1.5% precision in describing P3D and P1D from linear scales to k=5Mpc−1 and k∥=4Mpc−1, respectively. Thanks to its parameterization, the precision of the emulator is also similar for both ionization histories and two extensions to the ΛCDM model – massive neutrinos and curvature – not included in the training set. ForestFlow will be crucial for the cosmological analysis of Lyman-α forest measurements from the DESI survey.

We present the first measurements of Lyman-αα (Lyαα) forest correlations using early data from the Dark Energy Spectroscopic Instrument (DESI). We measure the auto-correlation of Lyαα absorption using 88,509 quasars at z>2z>2, and its cross-correlation with quasars using a further 147,899 tracer quasars at z≳1.77z≳1.77. Then, we fit these correlations using a 13-parameter model based on linear perturbation theory and find that it provides a good description of the data across a broad range of scales. We detect the BAO peak with a signal-to-noise ratio of 3.8σ3.8σ, and show that our measurements of the auto- and cross-correlations are fully-consistent with previous measurements by the Extended Baryon Oscillation Spectroscopic Survey (eBOSS). Even though we only use here a small fraction of the final DESI dataset, our uncertainties are only a factor of 1.7 larger than those from the final eBOSS measurement. We validate the existing analysis methods of Lyαα correlations in preparation for making a robust measurement of the BAO scale with the first year of DESI data.

This publication presents and validates the Lyman-alpha forest fluctuations in the first DESI data release. To accomplish this measurement, the continua of DESI quasars were fitted not only in the Lyman-alpha forest region but also in featureless regions to the right of the Lyman-alpha emission line, which were used for calibration.The image displays the observed flux (black) of a high-SNR DESI quasar. The different coloured lines show the expected flux for each of the regions (quasar continuum corrected by the mean absorption), for the Lyman-alpha forest region and the SIV, CIV and CIII calibration regions.For this publication, we followed the procedures designed for SDSS analyses and made necessary adaptations for the DESI pipeline. Additionally, we enhanced the weighting scheme, resulting in an improvement of over 20% in the precision of the correlation function measurement.

The Lyman-α offers a unique avenue for studying the distribution of matter in the high redshift universe and extracting precise …

We measure the expansion rate of the Universe at redshift z=2.3 from the anisotropy of Lyman-α (Lyα) forest correlations measured by …