Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory
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We present the cosmological implications from final measurements of clustering using galaxies, quasars, and $\mathrm{Ly}\ensuremath{\alpha}$ 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, $f{\ensuremath{\sigma}}_{8}$, 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, $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological model when combined with Planck measurements. The combined BAO and RSD measurements indicate ${\ensuremath{\sigma}}_{8}=0.85\ifmmode\pm\else\textpm\fi{}0.03$, 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Regardless of cosmological model, the precision on each of the three parameters, ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{\ensuremath{\Lambda}}}$, ${H}_{0}$, and ${\ensuremath{\sigma}}_{8}$, 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 ${\mathrm{\ensuremath{\Omega}}}_{k}=\ensuremath{-}0.0022\ifmmode\pm\else\textpm\fi{}0.0022$. The dark energy constraints lead to ${w}_{0}=\ensuremath{-}0.909\ifmmode\pm\else\textpm\fi{}0.081$ and ${w}_{a}=\ensuremath{-}0.4{9}_{\ensuremath{-}0.30}^{+0.35}$, corresponding to an equation of state of ${w}_{p}=\ensuremath{-}1.018\ifmmode\pm\else\textpm\fi{}0.032$ 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 ${H}_{0}=68.18\ifmmode\pm\else\textpm\fi{}0.79\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Our most constraining combination of data gives the upper limit on the sum of neutrino masses at $\ensuremath{\sum}{m}_{\ensuremath{\nu}}<0.115\text{ }\text{ }\mathrm{eV}$ (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 $w$, ${\mathrm{\ensuremath{\Omega}}}_{k}$, $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$, ${H}_{0}$, and ${\ensuremath{\sigma}}_{8}$ 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.
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The whole procedure leading to the BAO dataset may not necessarily be valid in extended DE models, where perturbations in the mildly nonlinear regime are important.
“the whole procedure leading to the BAO dataset performed by the different collaborations may not necessarily be valid in extended DE models, where perturbations in the mildly nonlinear regime are important.”
From Challenges of the Standard Cosmological Model (2022) · cites this paper as [15]
In the BAO measurement discussion (section “M H”; page unavailable), the paper calls its assumption about model dependence an approximation and notes sensitivity to the fiducial cosmology. It does not say that the BAO dataset procedure may be invalid in extended dark-energy models because mildly nonlinear perturbations are important. (LLM, conf=0.75)
Experimental — accuracy not yet measuredUsing Gaussian-process regression with a Matérn 5/2 kernel constrained by BAO nodes from eBOSS DR16 yields β=1.97±0.05 and γ0=(3.6±0.4)×10^97 kB.
“Using Gaussian-process regression with a Matérn 5/2 kernel constrained by BAO nodes from the eBOSS DR16 catalog [43], we obtainβ=1.97±0.05,γ0=(3.6±0.4)×1097kB.”
From Counting Cosmic Cycles: Past Big Crunches, Future Recurrence Limits, and the Age of the Quantum Memory Matrix Universe (2025) · cites this paper as [43]
BAO measurements from BOSS and eBOSS plus BBN data, assuming ΛCDM and CMB-independent, obtain a similar lower H0 value.
“a similar value is also obtained from the baryon acoustic oscillations (BAO) measurements from the BOSS and eBOSS estimates [15] plus the Big Bang nucleosynthesis (BBN) data, which assume a ΛCDM scenario and are CMB-independent.”
From Challenges of the Standard Cosmological Model (2022) · cites this paper as [15]
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Influential
- Authors
- Alam, S., Aubert, M., Avila, S., Balland, C., Bautista, J. E., Bershady, M. A., Bizyaev, D., Blanton, M. R., Bolton, A. S., Bovy, J., Brinkmann, J., Brownstein, J. R., Burtin, E., Chabanier, S., Chapman, M. J., Choi, P. D., Chuang, C.-H., Comparat, J., Cousinou, M.-C., Cuceu, A., Dawson, K. S., de la Torre, S., de Mattia, A., Agathe, V. D. S., des Bourboux, H. D. M., Escoffier, S., Etourneau, T., Farr, J., Font-Ribera, A., Frinchaboy, P. M., Fromenteau, S., Gil-Marín, H., Le Goff, J.-M., Gonzalez-Morales, A. X., Gonzalez-Perez, V., Grabowski, K., Guy, J., Hawken, A. J., Hou, J., Kong, H., Parker, J., Klaene, M., Kneib, J.-P., Lin, S., Long, D., Lyke, B. W., de la Macorra, A., Martini, P., Masters, K., Mohammad, F. G., Moon, J., Mueller, E.-M., Muñoz-Gutiérrez, A., Myers, A. D., Nadathur, S., Neveux, R., Newman, J. A., Noterdaeme, P., Oravetz, A., Oravetz, D., Palanque-Delabrouille, N., Pan, K., Paviot, R., Percival, W. J., Pérez-Ràfols, I., Petitjean, P., Pieri, M. M., Prakash, A., Raichoor, A., Ravoux, C., Rezaie, M., Rich, J., Ross, A. J., Rossi, G., Ruggeri, R., Ruhlmann-Kleider, V., Sánchez, A. G., Sánchez, F. J., Sánchez-Gallego, J. R., Sayres, C., Schneider, D. P., Seo, H.-J., Shafieloo, A., Slosar, A., Smith, A., Stermer, J., Tamone, A., Tinker, J. L., Tojeiro, R., Vargas-Magaña, M., Variu, A., Wang, Y., Weaver, B. A., Weijmans, A.-M., Yèche, C., Zarrouk, P., Zhao, C., Zhao, G.-B., & Zheng, Z.
- Affiliations
- University of Edinburgh (GB)
- Centre National de la Recherche Scientifique (FR)
- Consejo Superior de Investigaciones Científicas (ES)
- University of Portsmouth (GB)
- University of Wisconsin–Madison (US)
- New Mexico State University (US)
- New York University (US)
- University of Utah (US)
- University of Toronto (CA)
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- University of Waterloo (CA)
- Sejong University (KR)
- Kavli Institute for Particle Astrophysics and Cosmology (US)
- Max Planck Institute for Extraterrestrial Physics (DE)
- University College London (GB)
- Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
- IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
- University of Utah, Department of Physics and Astronomy, 115 S 1400 E, Salt Lake City, Utah 84112, USA
- Institute for High Energy Physics (ES)
- Texas Christian University (US)
- Universidad Nacional Autónoma de México (MX)
- Universitat de Barcelona (ES)
- División de Ciencias e Ingenierías, Universidad de Guanajuato, León 37150, México
- Liverpool John Moores University, L3 5RF Liverpool, United Kingdom
- Lawrence Berkeley National Laboratory (US)
- The Ohio State University (US)
- École Polytechnique Fédérale de Lausanne (CH)
- University of Wyoming (US)
- IFUNAM—Instituto de Física, Universidad Nacional Autónoma de México, 04510 CDMX, México
- Haverford College (US)
- University of Oxford (GB)
- University of Pittsburgh (US)
- California Institute of Technology (US)
- Ohio University (US)
- Swinburne University of Technology (AU)
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
- University of Washington (US)
- Pennsylvania State University (US)
- Korea Astronomy and Space Science Institute (KR)
- Brookhaven National Laboratory (US)
- Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fdrale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
- University of St Andrews (GB)
- Chinese Academy of Sciences (CN)
- NSF NOIRLab (US)
- Durham University (GB)
- ORCID
- Alam, Shadab
- Aubert, Marie
- Avila, Santiago
- Bautista, Julian E.
- Bershady, Matthew A.
- Bizyaev, Dmitry
- Blanton, Michael R.
- Bolton, Adam S.
- Bovy, Jo
- Brinkmann, Jonathan
- Brownstein, Joel R.
- Burtin, Etienne
- Chabanier, Solène
- Chuang, Chia-Hsun
- Comparat, Johan
- Cuceu, Andrei
- Dawson, Kyle S.
- Escoffier, Stephanie
- Font-Ribera, Andreu
- Frinchaboy, Peter M.
- Fromenteau, Sebastien
- Gil-Marín, Héctor
- Guy, Julien
- Hou, Jiamin
- Kong, Hui
- Kneib, Jean-Paul
- Lin, Sicheng
- Lyke, Brad W.
- Martini, Paul
- Masters, Karen
- Mohammad, Faizan G.
- Muñoz-Gutiérrez, Andrea
- Nadathur, Seshadri
- Newman, Jeffrey A.
- Noterdaeme, Pasquier
- Pan, Kaike
- Paviot, Romain
- Percival, Will J.
- Pérez-Ràfols, Ignasi
- Petitjean, Patrick
- Pieri, Matthew M.
- Prakash, Abhishek
- Raichoor, Anand
- Ravoux, Corentin
- Rezaie, Mehdi
- Rich, James
- Ross, Ashley J.
- Ruggeri, Rossana
- Ruhlmann-Kleider, Vanina
- Sánchez, Ariel G.
- Sánchez-Gallego, José R.
- Sayres, Conor
- Schneider, Donald P.
- Seo, Hee-Jong
- Shafieloo, Arman
- Slosar, Anže
- Smith, Alex
- Stermer, Julianna
- Tinker, Jeremy L.
- Tojeiro, Rita
- Vargas-Magaña, Mariana
- Variu, Andrei
- Wang, Yuting
- Weaver, Benjamin A.
- Weijmans, Anne-Marie
- Yèche, Christophe
- Zarrouk, Pauline
- Zhao, Cheng
- Zhao, Gong-Bo
- Zheng, Zheng
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2021-04-28
- Volume
- 103
- Issue
- 8
- Pages
- 083533
- ISSN
- 2470-0010 (ISSN-L)
- 2470-0029
- OpenAlex
- W3043102132
- Cited by
- 1,337
- References
- 307
- Citations by year
- 2026: 189 · 2025: 309 · 2024: 279 · 2023: 206 · 2022: 213 · 2021: 123 · 2020: 17
- FWCI
- 109.81
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical review. D/Physical review. D. (publishedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- eScholarship (California Digital Library) (submittedVersion)
- Biblos-e Archivo (Universidad Autónoma de Madrid) (submittedVersion, public-domain)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- St Andrews Research Repository (St Andrews Research Repository) (submittedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion)
- Hispana (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Alfred P. Sloan Foundation
- National Science Foundation
- Office of Science
- University of Utah
- Carnegie Mellon University
- Johns Hopkins University
- University of Tokyo
- Lawrence Berkeley National Laboratory
- Leibniz-Institut für Astrophysik Potsdam
- New Mexico State University
- New York University
- University of Notre Dame
- Ministério da Ciência, Tecnologia e Inovação
- Ohio State University
- Pennsylvania State University
- Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México
- University of Arizona
- University of Colorado Boulder
- University of Portsmouth
- University of Virginia
- University of Washington
- University of Wisconsin-Madison
- Vanderbilt University
- Yale University
- Instituto de Astrofísica de Canarias
- Kavli Institute for the Physics and Mathematics of the Universe
- Max-Planck-Institut für Astronomie
- Max-Planck-Institut für Astrophysik
- Max-Planck-Institut für Extraterrestrische Physik
- National Astronomical Observatory of China
- Shanghai Astronomical Observatory
- United Kingdom Participation Group
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
- Keywords
- baryon acoustic oscillations, large-scale structure, redshift-space distortions, structure growth, angular diameter distance, Hubble parameter, dark energy, cosmic curvature, LambdaCDM model, Lyman-alpha forest, quasar clustering, galaxy clustering, BOSS, Planck CMB constraints, weak gravitational lensing, Hubble constant
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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