We present the cosmological implications from final measurements of clustering using galaxies, quasars, and $\mathrm{Ly}\alpha$ 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, $r_d$, from eight different samples and six measurements of the growth rate parameter, $f{\sigma }_8$, 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, $\mathrm{\Lambda }\mathrm{CDM}$ 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 $\mathrm{\Lambda }\mathrm{CDM}$ cosmological model when combined with Planck measurements. The combined BAO and RSD measurements indicate ${\sigma }_8=0.85\pm 0.03$, 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 $\mathrm{\Lambda }\mathrm{CDM}$ model. Regardless of cosmological model, the precision on each of the three parameters, ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$, $H_0$, and ${\sigma }_8$, 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 ${\mathrm{\Omega }}_k=-0.0022\pm 0.0022$. The dark energy constraints lead to $w_0=-0.909\pm 0.081$ and $w_a=-0.49_{-0.30}^{+0.35}$, corresponding to an equation of state of $w_p=-1.018\pm 0.032$ at a pivot redshift $z_p=0.29$ and a Dark Energy Task Force Figure of Merit of 94. The inverse distance ladder measurement under this model yields $H_0=68.18\pm 0.79\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$, 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 $H_0$ that are independent of the CMB data, with similar central values and precision under a $\mathrm{\Lambda }\mathrm{CDM}$ model. Our most constraining combination of data gives the upper limit on the sum of neutrino masses at $\sum m_{\nu }<0.115\mathrm{eV}$ (95% confidence). Finally, we consider the improvements in cosmology constraints over the last decade by comparing our results to a sample representative of the period 2000–2010. We compute the relative gain across the five dimensions spanned by $w$, ${\mathrm{\Omega }}_k$, $\sum m_{\nu }$, $H_0$, and ${\sigma }_8$ and find that the SDSS BAO and RSD data reduce the total posterior volume by a factor of 40 relative to the previous generation. Adding again the Planck, DES, and Pantheon SN Ia samples leads to an overall contraction in the five-dimensional posterior volume of 3 orders of magnitude.

• Received 22 July 2020
• Accepted 16 March 2021

DOI:https://doi.org/10.1103/PhysRevD.103.083533