A flat Friedmann–Robertson–Walker universe dominated by a cosmological constant (Λ) and cold dark matter (CDM) has been the working model preferred by cosmologists since the discovery of cosmic acceleration1,2. However, tensions of various degrees of significance are known to be present among existing datasets within the ΛCDM framework3,4,5,6,7,8,9,10,11. In particular, the Lyman-α forest measurement of the baryon acoustic oscillations (BAO) by the Baryon Oscillation Spectroscopic Survey3 prefers a smaller value of the matter density fraction ΩM than that preferred by cosmic microwave background (CMB). Also, the recently measured value of the Hubble constant, H0 = 73.24 ± 1.74 km s−1 Mpc−1 (ref. 12), is 3.4σ higher than the 66.93 ± 0.62 km s−1 Mpc−1 inferred from the Planck CMB data7. In this work, we investigate whether these tensions can be interpreted as evidence for a non-constant dynamical dark energy. Using the Kullback–Leibler divergence13 to quantify the tension between datasets, we find that the tensions are relieved by an evolving dark energy, with the dynamical dark energy model preferred at a 3.5σ significance level based on the improvement in the fit alone. While, at present, the Bayesian evidence for the dynamical dark energy is insufficient to favour it over ΛCDM, we show that, if the current best-fit dark energy happened to be the true model, it would be decisively detected by the upcoming Dark Energy Spectroscopic Instrument survey14.

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G.-B.Z. is supported by National Natural Science Foundation of China (NSFC) Grant No. 11673025, and by a Royal Society-Newton Advanced Fellowship. G.-B.Z. and Y.W. are supported by National Astronomical Observatories, Chinese Academy of Sciences, and by University of Portsmouth. M.R. is supported by US Department of Energy contract DE-FG02-13ER41958. M.R. acknowledges partial support, during the development of this work, by the Italian Space Agency (ASI) through the ASI contracts Euclid-IC (I/031/10/0) and the INFN-INDARK initiative. M.R. thanks Scuola Internazionale Superiore di Studi Avanzati, where part of this work was completed. L.P. is supported by The Natural Sciences and Engineering Research Council of Canada, R.C. by Science and Technology Facilities Council grant ST/H002774/1, and Y.W. by NSFC Grant No. 11403034. G.R. acknowledges support from the National Research Foundation of Korea (NRF) through NRF-SGER 2014055950 funded by the Korean Ministry of Education, Science and Technology (MoEST), and from the faculty research fund of Sejong University in 2016. A.S. would like to acknowledge the support of the National Research Foundation of Korea (NRF - 2016R1C1B2016478). Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation and the US Department of Energy Office of Science. The SDSS-III website is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrosica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington and Yale University.

Author information


  1. National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012, China

    • Gong-Bo Zhao
    • , Yuting Wang
    •  & Hanyu Zhang
  2. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK

    • Gong-Bo Zhao
    • , Levon Pogosian
    • , Yuting Wang
    • , Robert G. Crittenden
    • , Will J. Percival
    • , Florian Beutler
    • , Kazuya Koyama
    • , Robert C. Nichol
    •  & Ashley J. Ross
  3. Kavli Institute for Cosmological Physics, Enrico Fermi Institute, The University of Chicago, Chicago, IL, 60637, USA

    • Marco Raveri
  4. Institute Lorentz, Leiden University, PO Box 9506, Leiden, 2300 RA, Netherlands

    • Marco Raveri
  5. Department of Physics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    • Levon Pogosian
  6. Astrophysics Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge, CB3 0HE, UK

    • Will J. Handley
  7. Kavli Institute for Cosmology, Madingley Road, Cambridge, CB3 0HA, UK

    • Will J. Handley
  8. Apache Point Observatory, PO Box 59, Sunspot, NM, 88349, USA

    • Jonathan Brinkmann
  9. Instituto de Física Teórica, (UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, Madrid, E-28049, Spain

    • Chia-Hsun Chuang
    •  & Sergio Rodriguez-Torres
  10. Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482, Potsdam, Germany

    • Chia-Hsun Chuang
  11. Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC- UB), Martí i Franquès 1, Barcelona, E-08028, Spain

    • Antonio J. Cuesta
  12. Departamento de Física, Universidad de Córdoba, Campus de Rabanales, Edificio Albert Einstein, Córdoba, E-14071, Spain

    • Antonio J. Cuesta
  13. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA, 02138, USA

    • Daniel J. Eisenstein
  14. Instituto de Astrofísica de Canarias, 38205 San Crist obal de La Laguna, Santa Cruz de Tenerife, Spain

    • Francisco-Shu Kitaura
  15. Departamento de Astrofísica, Universidad de La Laguna (ULL), La Laguna, Tenerife, E-38206, Spain

    • Francisco-Shu Kitaura
  16. Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon, 34055, Korea

    • Benjamin L’Huillier
    •  & Arman Shafieloo
  17. Aix Marseille Université, CNRS, Laboratoire d’Astrophysique de Marseille, UMR 7326, Marseille, 13388, France

    • Matthew M. Pieri
  18. Campus of International Excellence UAM+CSIC, Cantoblanco, Madrid, E-28049, Spain

    • Sergio Rodriguez-Torres
  19. Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, Madrid, E-28049, Spain

    • Sergio Rodriguez-Torres
  20. Center for Cosmology and AstroParticle Physics, The Ohio State University, Columbus, OH, 43210, USA

    • Ashley J. Ross
  21. Department of Astronomy and Space Science, Sejong University, Seoul, 143-747, Korea

    • Graziano Rossi
  22. Max-Planck-Institut für extraterrestrische Physik, Postfach 1312, Giessenbachstraße, 85741, Garching, Germany

    • Ariel G. Sánchez
  23. University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon, 34113, Korea

    • Arman Shafieloo
  24. Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY, 10003, USA

    • Jeremy L. Tinker
  25. School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK

    • Rita Tojeiro
  26. Brookhaven National Laboratory, Building 510, Upton, NY, 11973, USA

    • Jose A. Vazquez


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G.-B.Z. proposed the idea, performed the dark energy reconstruction, evidence calculation, principal-component analysis and tension calculation. M.R. and Y.W. contributed to the tension calculation. G.-B.Z. and L.P. wrote the draft, and all other co-authors commented on and helped to improve the manuscript and/or contributed to the BOSS data analysis.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Gong-Bo Zhao.

Electronic supplementary material

  1. Supplementary Information

    Supplementary Tables 1–3, Supplementary Figures 1–5 and Supplementary References