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We present the cosmological implications from final measurements of clustering using galaxies, quasars, and Lyα forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of data from SDSS, SDSS-II, BOSS, and eBOSS, offer independent measurements of baryon acoustic oscillation (BAO) measurements of angular-diameter distances and Hubble distances relative to the sound horizon, rd, from eight different samples and six measurements of the growth rate parameter, fσ8, from redshift-space distortions (RSD). This composite sample is the most constraining of its kind and allows us to perform a comprehensive assessment of the cosmological model after two decades of dedicated spectroscopic observation. We show that the BAO data alone are able to rule out dark-energy-free models at more than eight standard deviations in an extension to the flat, ΛCDM model that allows for curvature. When combined with Planck Cosmic Microwave Background (CMB) measurements of temperature and polarization, under the same model, the BAO data provide nearly an order of magnitude improvement on curvature constraints relative to primary CMB constraints alone. Independent of distance measurements, the SDSS RSD data complement weak lensing measurements from the Dark Energy Survey (DES) in demonstrating a preference for a flat ΛCDM cosmological model when combined with Planck measurements. The combined BAO and RSD measurements indicate σ8=0.85±0.03, implying a growth rate that is consistent with predictions from Planck temperature and polarization data and with General Relativity. When combining the results of SDSS BAO and RSD, Planck, Pantheon Type Ia supernovae (SNe Ia), and DES weak lensing and clustering measurements, all multiple-parameter extensions remain consistent with a ΛCDM model. Regardless of cosmological model, the precision on each of the three parameters, ωΛ, H0, and σ8, remains at roughly 1%, showing changes of less than 0.6% in the central values between models. In a model that allows for free curvature and a time-evolving equation of state for dark energy, the combined samples produce a constraint ωk=-0.0022±0.0022. The dark energy constraints lead to w0=-0.909±0.081 and wa=-0.49-0.30+0.35, corresponding to an equation of state of wp=-1.018±0.032 at a pivot redshift zp=0.29 and a Dark Energy Task Force Figure of Merit of 94. The inverse distance ladder measurement under this model yields H0=68.18±0.79 km s-1 Mpc-1, remaining in tension with several direct determination methods; the BAO data allow Hubble constant estimates that are robust against the assumption of the cosmological model. In addition, the BAO data allow estimates of H0 that are independent of the CMB data, with similar central values and precision under a ΛCDM model. Our most constraining combination of data gives the upper limit on the sum of neutrino masses at mν

We derive constraints on cosmological parameters and tests of dark energy models from the combination of baryon acoustic oscillation (BAO) measurements with cosmic microwave background (CMB) data and a recent reanalysis of Type Ia supernova (SN) data. In particular, we take advantage of high-precision BAO measurements from galaxy clustering and the Lyman-α forest (LyaF) in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). Treating the BAO scale as an uncalibrated standard ruler, BAO data alone yield a high confidence detection of dark energy; in combination with the CMB angular acoustic scale they further imply a nearly flat universe. Adding the CMB-calibrated physical scale of the sound horizon, the combination of BAO and SN data into an "inverse distance ladder" yields a measurement of H0=67.3±1.1 km s-1 Mpc-1, with 1.7% precision. This measurement assumes standard prerecombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat ΛCDM cosmology is an important corroboration of this minimal cosmological model. For constant dark energy (Λ), our BAO+SN+CMB combination yields matter density Ωm=0.301±0.008 and curvature Ωk=-0.003±0.003. When we allow more general forms of evolving dark energy, the BAO+SN+CMB parameter constraints are always consistent with flat ΛCDM values at ≈1σ. While the overall χ2 of model fits is satisfactory, the LyaF BAO measurements are in moderate (2-2.5σ) tension with model predictions. Models with early dark energy that tracks the dominant energy component at high redshift remain consistent with our expansion history constraints, and they yield a higher H0 and lower matter clustering amplitude, improving agreement with some low redshift observations. Expansion history alone yields an upper limit on the summed mass of neutrino species, mν