We present cosmological results from the final galaxy clustering data set of the Baryon Oscillation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. Our combined galaxy sample comprises 1.2 million massive galaxies over an effective area of 9329 deg² and volume of 18.7 Gpc³, divided into three partially overlapping redshift slices centred at effective redshifts 0.38, 0.51 and 0.61. We measure the angular diameter distance D_M and Hubble parameter H from the baryon acoustic oscillation (BAO) method, in combination with a cosmic microwave background prior on the sound horizon scale, after applying reconstruction to reduce non-linear effects on the BAO feature. Using the anisotropic clustering of the pre-reconstruction density field, we measure the product D_MH from the Alcock–Paczynski (AP) effect and the growth of structure, quantified by fσ₈(z), from redshift-space distortions (RSD). We combine individual measurements presented in seven companion papers into a set of consensus values and likelihoods, obtaining constraints that are tighter and more robust than those from any one method; in particular, the AP measurement from sub-BAO scales sharpens constraints from post-reconstruction BAOs by breaking degeneracy between D_M and H. Combined with Planck 2016 cosmic microwave background measurements, our distance scale measurements simultaneously imply curvature Ω_K = 0.0003 ± 0.0026 and a dark energy equation-of-state parameter w = −1.01 ± 0.06, in strong affirmation of the spatially flat cold dark matter (CDM) model with a cosmological constant (ΛCDM). Our RSD measurements of fσ₈, at 6 per cent precision, are similarly consistent with this model. When combined with supernova Ia data, we find H₀ = 67.3 ± 1.0 km s⁻¹ Mpc⁻¹ even for our most general dark energy model, in tension with some direct measurements. Adding extra relativistic species as a degree of freedom loosens the constraint only slightly, to H₀ = 67.8 ± 1.2 km s⁻¹ Mpc⁻¹. Assuming flat ΛCDM, we find Ω_m = 0.310 ± 0.005 and H₀ = 67.6 ± 0.5 km s⁻¹ Mpc⁻¹, and we find a 95 per cent upper limit of 0.16 eV c⁻² on the neutrino mass sum.

We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations (BAO) in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey, which is part of the Sloan Digital Sky Survey III. Our results come from the Data Release 11 (DR11) sample, containing nearly one million galaxies and covering approximately 8500 square degrees and the redshift range 0.2 < $$z$$ < 0.7. We also compare these results with those from the publicly released DR9 and DR10 samples. Assuming a concordance Λ cold dark matter (ΛCDM) cosmological model, the DR11 sample covers a volume of 13 Gpc³ and is the largest region of the Universe ever surveyed at this density. We measure the correlation function and power spectrum, including density-field reconstruction of the BAO feature. The acoustic features are detected at a significance of over 7σ in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, r_d, which has a value of r_d,fid = 149.28 Mpc in our fiducial cosmology. We find D_V = (1264 ± 25 Mpc)(r_d/r_d,fid) at $$z$$ = 0.32 and D_V = (2056 ± 20 Mpc)(r_d/r_d,fid) at $$z$$ = 0.57. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line of sight yields measurements at $$z$$ = 0.57 of D_A = (1421 ± 20 Mpc)(r_d/r_d,fid) and H = (96.8 ± 3.4 km s⁻¹ Mpc⁻¹)(r_d,fid/r_d). Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat CDM model with a cosmological constant.

We describe the Sloan Digital Sky Survey IV (SDSS-IV), a project encompassing three major spectroscopic programs. The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is observing hundreds of thousands of Milky Way stars at high resolution and high signal-to-noise ratios in the near-infrared. The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey is obtaining spatially resolved spectroscopy for thousands of nearby galaxies (median ). The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is mapping the galaxy, quasar, and neutral gas distributions between and 3.5 to constrain cosmology using baryon acoustic oscillations, redshift space distortions, and the shape of the power spectrum. Within eBOSS, we are conducting two major subprograms: the SPectroscopic IDentification of eROSITA Sources (SPIDERS), investigating X-ray AGNs and galaxies in X-ray clusters, and the Time Domain Spectroscopic Survey (TDSS), obtaining spectra of variable sources. All programs use the 2.5 m Sloan Foundation Telescope at the Apache Point Observatory; observations there began in Summer 2014. APOGEE-2 also operates a second near-infrared spectrograph at the 2.5 m du Pont Telescope at Las Campanas Observatory, with observations beginning in early 2017. Observations at both facilities are scheduled to continue through 2020. In keeping with previous SDSS policy, SDSS-IV provides regularly scheduled public data releases; the first one, Data Release 13, was made available in 2016 July.

The Sloan Digital Sky Survey III (SDSS-III) presents the first spectroscopic data from the Baryon Oscillation Spectroscopic Survey (BOSS). This ninth data release (DR9) of the SDSS project includes 535,995 new galaxy spectra (median z ∼ 0.52), 102,100 new quasar spectra (median z ∼ 2.32), and 90,897 new stellar spectra, along with the data presented in previous data releases. These spectra were obtained with the new BOSS spectrograph and were taken between 2009 December and 2011 July. In addition, the stellar parameters pipeline, which determines radial velocities, surface temperatures, surface gravities, and metallicities of stars, has been updated and refined with improvements in temperature estimates for stars with T _eff < 5000 K and in metallicity estimates for stars with [Fe/H] > -0.5. DR9 includes new stellar parameters for all stars presented in DR8, including stars from SDSS-I and II, as well as those observed as part of the SEGUE-2. The astrometry error introduced in the DR8 imaging catalogs has been corrected in the DR9 data products. The next data release for SDSS-III will be in Summer 2013, which will present the first data from the APOGEE along with another year of data from BOSS, followed by the final SDSS-III data release in 2014 December.