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  1. Data Release 1 of the Dark Energy Spectroscopic Instrument

    In 2021 May the Dark Energy Spectroscopic Instrument (DESI) collaboration began a 5 yr spectroscopic redshift survey to produce a detailed map of the evolving three-dimensional structure of the Universe between z = 0 and z ≈ 4. DESI’s principal scientific objectives are to place precise constraints on the equation of state of dark energy, the gravitationally driven growth of large-scale structure, and the sum of the neutrino masses, and to explore the observational signatures of primordial inflation. We present DESI DR1, which consists of all data acquired during the first 13 months of the DESI main survey, as well as amore » uniform reprocessing of the DESI Survey Validation data, which were previously made public in the DESI Early Data Release. The DR1 main survey includes high-confidence redshifts for 18.7M objects, of which 13.1M are spectroscopically classified as galaxies, 1.6M as quasars, and 4M as stars, making DR1 the largest sample of extragalactic redshifts ever assembled. We summarize the DR1 observations, the spectroscopic data-reduction pipeline and data products, large-scale structure catalogs, value-added catalogs, and describe how to access and interact with the data. In addition to fulfilling its core cosmological objectives with unprecedented precision, we expect DR1 to enable a wide range of transformational astrophysical studies and discoveries.« less
  2. DESI DR2 results. I. Baryon acoustic oscillations from the Lyman alpha forest

    We present the baryon acoustic oscillation (BAO) measurements with the Lyman-𝛼 (Ly⁢𝛼) forest from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI) survey. Our BAO measurements include both the autocorrelation of the Ly⁢𝛼 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 2 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 twomore » supporting papers describe improvements to the synthetic datasets that we use for validation and how we identify damped Ly⁢𝛼 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 =2.33. 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 Ly⁢𝛼 BAO analysis for the first time. We measure the ratios 𝐷𝐻⁡(𝑧eff)/𝑟𝑑 = 8.632 ± 0.098 ± 0.026 and 𝐷𝑀⁡(𝑧eff)/𝑟𝑑 = 38.99 ± 0.52 ± 0.12, where 𝐷𝐻 = 𝑐/𝐻⁡(𝑧) is the Hubble distance, 𝐷𝑀 is the transverse comoving distance, 𝑟𝑑 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.« less
  3. DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints

    We present baryon acoustic oscillation (BAO) measurements from more than 14 million galaxies and quasars drawn from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), based on three years of operation. For cosmology inference, these galaxy measurements are combined with DESI Lyman-𝛼 forest BAO results presented in a companion paper (M. Abdul-Karim et al., companion paper, Phys. Rev. D 112, 083514 2025.). The DR2 BAO results are consistent with DESI DR1 and the Sloan Digital Sky Survey, and their distance-redshift relationship matches those from recent compilations of supernovae (SNe) over the same redshift range. The results are wellmore » described by a flat Λ cold dark matter (Λ⁢CDM) model, but the parameters preferred by BAO are in mild, 2.3⁢𝜎 tension with those determined from the cosmic microwave background (CMB), although the DESI results are consistent with the acoustic angular scale 𝜃* that is well measured by Planck. This tension is alleviated by dark energy with a time-evolving equation of state parametrized by 𝑤0 and 𝑤𝑎, which provides a better fit to the data, with a favored solution in the quadrant with 𝑤0 >−1 and 𝑤𝑎 <0. This solution is preferred over Λ ⁢CDM at 3.1⁢𝜎 for the combination of DESI BAO and CMB data. When also including SNe, the preference for a dynamical dark energy model over Λ⁢ CDM ranges from 2.8 − 4.2⁢𝜎 depending on which SNe sample is used. We present evidence from other data combinations which also favor the same behavior at high significance. From the combination of DESI and CMB we derive 95% upper limits on the sum of neutrino masses, finding ∑𝑚𝜈 < 0.064 eV assuming Λ ⁢CDM and ∑𝑚𝜈 < 0.16 eV in the 𝑤0⁢𝑤𝑎 model. Unless there is an unknown systematic error associated with one or more datasets, it is clear that Λ⁢ CDM is being challenged by the combination of DESI BAO with other measurements and that dynamical dark energy offers a possible solution.« less
  4. Validation of the DESI DR2 measurements of baryon acoustic oscillations from galaxies and quasars

    The Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) galaxy and quasar clustering data represents a significant expansion of data from Data Release 1 (DR1), providing improved statistical precision in baryon acoustic oscillation (BAO) constraints across multiple tracers, including bright galaxies, luminous red galaxies, emission line galaxies, and quasars. In this paper, we validate the BAO analysis of DR2. We present the results of robustness tests on the blinded DR2 data and, after unblinding, consistency checks on the unblinded DR2 data. All results are compared with those obtained from a suite of mock catalogs that replicate the selection andmore » clustering properties of the DR2 sample. We confirm the consistency of DR2 BAO measurements with DR1 while achieving a reduction in statistical uncertainties due to the increased survey volume and completeness. The combined BAO precision, including both statistical and systematic errors, improves from ∼0.52% in DR1 to 0.30% in DR2—a factor of 1.7 gain. We assess the impact of analysis choices, including different data vectors (correlation function vs power spectrum), modeling approaches and systematics treatments, and an assumption of the Gaussian likelihood, finding that our BAO constraints are stable across these variations and assumptions with a few minor refinements to the baseline setup of the DR1 BAO analysis. We summarize a series of pre-unblinding tests that confirmed the readiness of our analysis pipeline, the final systematic errors, and the DR2 BAO analysis baseline. The successful completion of these tests led to the unblinding of the DR2 BAO measurements, ultimately leading to the DESI DR2 cosmological analysis, with their implications for the expansion history of the Universe and the nature of dark energy presented in the DESI key paper (companion paper).« less
  5. DESI 2024 V: Full-Shape galaxy clustering from galaxies and quasars

    We present the measurements and cosmological implications of the galaxy two-point clustering using over 4.7 million unique galaxy and quasar redshifts in the range 0.1 < z < 2.1 divided into six redshift bins over a ∼ 7,500 square degree footprint, from the first year of observations with the Dark Energy Spectroscopic Instrument (DESI Data Release 1). By fitting the full power spectrum, we extend previous DESI DR1 baryon acoustic oscillation (BAO) measurements to include redshift-space distortions and signals from the matter-radiation equality scale. For the first time, this Full-Shape analysis is blinded at the catalogue-level to avoid confirmation biasmore » and the systematic errors are accounted for at the two-point clustering level, which automatically propagates them into any cosmological parameter. When analyzing the data in terms of compressed model-agnostic variables, we obtain a combined precision of 4.7% on the amplitude of the redshift space distortion (RSD) signal reaching a similar precision with just one year of DESI data than with twenty years of observation from the previous generation survey. We also analyze the data to directly constrain the cosmological parameters within the ΛCDM model using perturbation theory and combine this information with the reconstructed DESI DR1 galaxy BAO. Using a Big Bang Nucleosynthesis Gaussian prior on the baryon density parameter, ωb, and a weak Gaussian prior on the spectral index, ns, we constrain the matter density is Ωm = 0.296±0.010 and the Hubble constant H0 = (68.63 ± 0.79)[km s-1Mpc-1]. Additionally, we measure the amplitude of clustering σ8 = 0.841±0.034. The DESI DR1 galaxy clustering results are in agreement with the ΛCDM model based on general relativity with parameters consistent with those from Planck. The cosmological interpretation of these results in combination with DESI DR1 Ly-α forest data and external datasets are presented in the companion paper [1].« less
  6. DESI 2024 VII: cosmological constraints from the full-shape modeling of clustering measurements

    We present cosmological results from the measurement of clustering of galaxy, quasar and Lyman-α forest tracers from the first year of observations with the Dark Energy Spectroscopic Instrument (DESI Data Release 1). We adopt the full-shape (FS) modeling of the power spectrum, including the effects of redshift-space distortions, in an analysis which has been thoroughly validated in a series of supporting papers as summarised in [1]. We combine the full-shape information with DESI's DR1 constraints from the baryon acoustic oscillations (BAO) of these tracers. In the flat ΛCDM cosmological model, DESI (FS+BAO), combined with a baryon density prior from Bigmore » Bang Nucleosynthesis and a weak prior on the scalar spectral index, determines matter density to Ωm = 0.2962 ± 0.0095, and the amplitude of mass fluctuations to σ8 = 0.842 ± 0.034. The addition of the cosmic microwave background (CMB) data tightens these constraints to Ωm = 0.3056 ± 0.0049 and σ8 = 0.8121 ± 0.0053, while further addition of the joint clustering and lensing analysis from the Dark Energy Survey Year-3 (DESY3) data further improves these measurements, and leads to a 0.4% determination of the Hubble constant, H0 = (68.40 ± 0.27) km s-1 Mpc-1. In models with a time-varying dark energy equation of state parametrised by w0 and wa, combinations of DESI (FS+BAO) with CMB and type Ia supernovae continue to show the preference, previously found in the DESI DR1 BAO analysis, for w0 > -1 and wa < 0 with similar levels of significance. DESI data, in combination with the CMB, improve the upper limits on the sum of the neutrino masses relative to the case when only the DR1 BAO was available, giving ∑mν < 0.071 eV at 95% confidence. We finally constrain deviations from general relativity represented by two modified gravity parameters. DESI (FS+BAO) data alone measure the parameter that controls the clustering of massive particles, μ0 = 0.11+0.45-0.54, in agreement with the zero value predicted by general relativity. The combination of DESI with the CMB and the clustering and lensing analysis from DESY3 constrains both modified-gravity parameters, giving μ0 = 0.04 ± 0.22 and Σ0 = 0.044 ± 0.047, again in agreement with general relativity.« less
  7. DESI 2024 II: sample definitions, characteristics, and two-point clustering statistics

    We present the samples of galaxies and quasars used for DESI 2024 cosmological analyses, drawn from the DESI Data Release 1 (DR1). We describe the construction of largescale structure (LSS) catalogs from these samples, which include matched sets of synthetic reference ‘randoms’ and weights that account for variations in the observed density of the samples due to experimental design and varying instrument performance. We detail how we correct for variations in observational completeness, the input ‘target’ densities due to imaging systematics, and the ability to confidently measure redshifts from DESI spectra. We then summarize how remaining uncertainties in the correctionsmore » can be translated to systematic uncertainties for particular analyses. We describe the weights added to maximize the signalto-noise of DESI DR1 2-point clustering measurements. We detail measurement pipelines applied to the LSS catalogs that obtain 2-point clustering measurements in configuration and Fourier space. The resulting 2-point measurements depend on window functions and normalization constraints particular to each sample, and we present the corrections required to match models to the data. We compare the configuration- and Fourier-space 2-point clustering of the data samples to that recovered from simulations of DESI DR1 and find they are, generally, in statistical agreement to within 2% in the inferred real-space over-density field. The LSS catalogs, 2-point measurements, and their covariance matrices will be released publicly with DESI DR1.« less
  8. DESI DR2 Results I: Baryon Acoustic Oscillations from the Lyman Alpha Forest

    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 twomore » 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 $$z_{eff} = 2.33$$. 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 $$D_H(z_{eff})/r_d = 8.632 \pm 0.098 \pm 0.026$$ and $$D_M(z_{eff})/r_d = 38.99 \pm 0.52 \pm 0.12$$, where $$D_H = c/H(z)$$ is the Hubble distance, $$D_M$$ is the transverse comoving distance, $$r_d$$ 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.« less
  9. DESI 2024 III: baryon acoustic oscillations from galaxies and quasars

    We present the DESI 2024 galaxy and quasar baryon acoustic oscillations (BAO) measurements using over 5.7 million unique galaxy and quasar redshifts in the range 0.1 < z < 2.1. Divided by tracer type, we utilize 300,017 galaxies from the magnitude-limited Bright Galaxy Survey with 0.1 < z < 0.4, 2,138,600 Luminous Red Galaxies with 0.4 < z < 1.1, 2,432,022 Emission Line Galaxies with 0.8 < z < 1.6, and 856,652 quasars with 0.8 < z < 2.1, over a ∼ 7,500 square degree footprint. The analysis was blinded at the catalog-level to avoid confirmation bias. All fiducial choicesmore » of the BAO fitting and reconstruction methodology, as well as the size of the systematic errors, were determined on the basis of the tests with mock catalogs and the blinded data catalogs. We present several improvements to the BAO analysis pipeline, including enhancing the BAO fitting and reconstruction methods in a more physically-motivated direction, and also present results using combinations of tracers. We employ a unified BAO analysis method across all tracers. We present a re-analysis of SDSS BOSS and eBOSS results applying the improved DESI methodology and find scatter consistent with the level of the quoted SDSS theoretical systematic uncertainties. With the total effective survey volume of ∼ 18 Gpc3, the combined precision of the BAO measurements across the six different redshift bins is ∼0.52%, marking a 1.2-fold improvement over the previous state-of-the-art results using only first-year data. We detect the BAO in all of these six redshift bins. The highest significance of BAO detection is 9.1σ at the effective redshift of 0.93, with a constraint of 0.86% placed on the BAO scale. We find that our observed BAO scales are systematically larger than the prediction of the Planck 2018-ΛCDM at z < 0.8. We translate the results into transverse comoving distance and radial Hubble distance measurements, which are used to constrain cosmological models in our companion paper.« less
  10. DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations

    We present cosmological results from the measurement of baryon acoustic oscillations (BAO) in galaxy, quasar and Lyman-α forest tracers from the first year of observations from the Dark Energy Spectroscopic Instrument (DESI), to be released in the DESI Data Release 1. DESI BAO provide robust measurements of the transverse comoving distance and Hubble rate, or their combination, relative to the sound horizon, in seven redshift bins from over 6 million extragalactic objects in the redshift range 0.1 < z < 4.2. To mitigate confirmation bias, a blind analysis was implemented to measure the BAO scales. DESI BAO data alone aremore » consistent with the standard flat ΛCDM cosmological model with a matter density Ωm=0.295±0.015. Paired with a baryon density prior from Big Bang Nucleosynthesis and the robustly measured acoustic angular scale from the cosmic microwave background (CMB), DESI requires H0=(68.52±0.62) km s-1 Mpc-1. In conjunction with CMB anisotropies from Planck and CMB lensing data from Planck and ACT, we find Ωm=0.307± 0.005 and H0=(67.97±0.38) km s-1 Mpc-1. Extending the baseline model with a constant dark energy equation of state parameter w, DESI BAO alone requirew=-0.99+0.15-0.13. In models with a time-varying dark energy equation of state parametrised by w0 and wa, combinations of DESI with CMB or with type Ia supernovae (SN Ia) individually prefer w0 > -1 and wa < 0. This preference is 2.6σ for the DESI+CMB combination, and persists or grows when SN Ia are added in, giving results discrepant with the ΛCDM model at the 2.5σ, 3.5σ or 3.9σ levels for the addition of the Pantheon+, Union3, or DES-SN5YR supernova datasets respectively. For the flat ΛCDM model with the sum of neutrino mass ∑ mν free, combining the DESI and CMB data yields an upper limit ∑ mν < 0.072 (0.113) eV at 95% confidence for a ∑ mν > 0 (∑ mν > 0.059) eV prior. These neutrino-mass constraints are substantially relaxed if the background dynamics are allowed to deviate from flat ΛCDM.« less
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