We present the cosmological implications from final measurements of clustering using galaxies , quasars , and 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 , \Lambda 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 \Lambda CDM cosmological model when combined with Planck measurements .
The RSD and lensing measurements indicate 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 \Lambda CDM model .
Regardless of cosmological model , the precision on each of the three \Lambda CDM parameters , \Omega _ { \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 \Omega _ { k } = -0.0023 \pm 0.0022 .
The dark energy constraints lead to w _ { 0 } = -0.912 \pm 0.081 and w _ { a } = -0.48 ^ { +0.36 } _ { -0.30 } , corresponding to an equation of state of w _ { p } = -1.020 \pm 0.032 at a pivot redshift z _ { p } = 0.29 and a Dark Energy Figure of Merit of 92 .
The inverse distance ladder measurement under this model yields H _ { 0 } = 68.20 \pm 0.81 { 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 H _ { 0 } that are independent of the CMB data , with similar central values and precision under a \Lambda CDM model .
Our most constraining combination of data gives the upper limit on the sum of neutrino masses at \sum m _ { \nu } < 0.111 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 , \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 three orders of magnitude .