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We present the cosmological implications from final measurements ofclustering using galaxies, quasars, and Ly$\alpha$ forests from the completedSloan Digital Sky Survey (SDSS) lineage of experiments in large-scalestructure. These experiments, composed of data from SDSS, SDSS-II, BOSS, andeBOSS, offer independent measurements of baryon acoustic oscillation (BAO)measurements of angular-diameter distances and Hubble distances relative to thesound horizon, $r_d$, from eight different samples and six measurements of thegrowth rate parameter, $f\sigma_8$, from redshift-space distortions (RSD). Thiscomposite sample is the most constraining of its kind and allows us to performa comprehensive assessment of the cosmological model after two decades ofdedicated spectroscopic observation. We show that the BAO data alone are ableto rule out dark-energy-free models at more than eight standard deviations inan extension to the flat, $\Lambda$CDM model that allows for curvature. Whencombined with Planck Cosmic Microwave Background (CMB) measurements oftemperature and polarization the BAO data provide nearly an order of magnitudeimprovement on curvature constraints. The RSD measurements indicate a growthrate that is consistent with predictions from Planck primary data and withGeneral Relativity. When combining the results of SDSS BAO and RSD withexternal data, all multiple-parameter extensions remain consistent with a$\Lambda$CDM model. Regardless of cosmological model, the precision on$\Omega_\Lambda$, $H_0$, and $\sigma_8$, remains at roughly 1\%, showingchanges of less than 0.6\% in the central values between models. The inversedistance ladder measurement under a o$w_0w_a$CDM yields $H_0= 68.20 \pm 0.81 \,\rm km\, s^{-1} Mpc^{-1}$, remaining in tension with several directdetermination methods. (abridged)

physical review. d/physical review. d.

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey:  Cosmological Implications from two Decades of Spectroscopic Surveys at the  Apache Point observatory