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 are consistent with the standard flat ΛCDM cosmological model with a matter density Ω_m=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 H ₀=(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 Ω_m=0.307± 0.005 and H ₀=(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 require w=-0.99^+0.15 _-0.13. In models with a time-varying dark energy equation of state parametrised by w ₀ and w_a , combinations of DESI with CMB or with type Ia supernovae (SN Ia) individually prefer w ₀ > -1 and w_a < 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 ∑ m_ν free, combining the DESI and CMB data yields an upper limit ∑ m_ν < 0.072 (0.113) eV at 95% confidence for a ∑ m_ν > 0 (∑ m_ν > 0.059) eV prior. These neutrino-mass constraints are substantially relaxed if the background dynamics are allowed to deviate from flat ΛCDM.

This paper documents the 16th data release (DR16) from the Sloan Digital Sky Surveys (SDSS), the fourth and penultimate from the fourth phase (SDSS-IV). This is the first release of data from the Southern Hemisphere survey of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2); new data from APOGEE-2 North are also included. DR16 is also notable as the final data release for the main cosmological program of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and all raw and reduced spectra from that project are released here. DR16 also includes all the data from the Time Domain Spectroscopic Survey and new data from the SPectroscopic IDentification of ERosita Survey programs, both of which were co-observed on eBOSS plates. DR16 has no new data from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey (or the MaNGA Stellar Library “MaStar”). We also preview future SDSS-V operations (due to start in 2020), and summarize plans for the final SDSS-IV data release (DR17).

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 , companion paper, .). 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 well 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 w 0 and w a , which provides a better fit to the data, with a favored solution in the quadrant with w 0 > − 1 and w a < 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 ∑ m ν < 0.064 eV assuming Λ CDM and ∑ m ν < 0.16 eV in the w 0 w a 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.

We introduce two new diagnostics of dark energy (DE). The first, $Om$, is a combination of the Hubble parameter and the cosmological redshift and provides a null test of dark energy being a cosmological constant $\Lambda$. Namely, if the value of $Om(z)$ is the same at different redshifts, then $\mathrm{DE}\equiv \Lambda$, exactly. The slope of $Om(z)$ can differentiate between different models of dark energy even if the value of the matter density is not accurately known. For DE with an unevolving equation of state, a positive slope of $Om(z)$ is suggestive of phantom ($w<-1$) while a negative slope indicates quintessence ($w>-1$). The second diagnostic—acceleration probe $\overline{q}$—is the mean value of the deceleration parameter over a small redshift range. It can be used to determine the cosmological redshift at which the universe began to accelerate, again without reference to the current value of the matter density. We apply the $Om$ and $\overline{q}$ diagnostics to the Union data set of type Ia supernovae combined with recent data from the cosmic microwave background (Wilkinson Microwave Anisotropy Probe 5) and baryon acoustic oscillations.

The Dark Energy Spectroscopic Instrument (DESI) completed its 5 month Survey Validation in 2021 May. Spectra of stellar and extragalactic targets from Survey Validation constitute the first major data sample from the DESI survey. This paper describes the public release of those spectra, the catalogs of derived properties, and the intermediate data products. In total, the public release includes good-quality spectral information from 466,447 objects targeted as part of the Milky Way Survey, 428,758 as part of the Bright Galaxy Survey, 227,318 as part of the Luminous Red Galaxy sample, 437,664 as part of the Emission Line Galaxy sample, and 76,079 as part of the Quasar sample. In addition, the release includes spectral information from 137,148 objects that expand the scope beyond the primary samples as part of a series of secondary programs. Here, we describe the spectral data, data quality, data products, Large-Scale Structure science catalogs, access to the data, and references that provide relevant background to using these spectra.