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Dynamical dark energy in light of the latest observations

Nature Astronomy volume 1, pages 627–632 (2017)Cite this article

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Abstract

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 Ω M than that preferred by cosmic microwave background (CMB). Also, the recently measured value of the Hubble constant, H 0 = 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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Fig. 1: The tension among different datasets in ΛCDM and w(z)CDM universes.
Fig. 2: Reconstructed evolution history of the dark energy equation of state compared with the 2012 result and the forecasted uncertainty from future data.
Fig. 3: The Bayes factor and the significance level of w ≠ −1 for various correlated priors for current and future data.

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References

  1. Riess, A. G. et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998).

    Article  ADS  Google Scholar 

  2. Perlmutter, S. et al. Measurements of Ω and Λ from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999).

    Article  ADS  MATH  Google Scholar 

  3. Delubac, T. et al. Baryon acoustic oscillations in the Lyα forest of BOSS DR11 quasars. Astron. Astrophys. 574, A59 (2015).

    Article  Google Scholar 

  4. Sahni, V., Shafieloo, A. & Starobinsky, A. A. Model-independent evidence for dark energy evolution from baryon acoustic oscillations. Astrophys. J. Lett. 793, L40 (2014).

    Article  ADS  Google Scholar 

  5. Battye, R. A., Charnock, T. & Moss, A. Tension between the power spectrum of density perturbations measured on large and small scales. Phys. Rev. D 91, 103508 (2015).

    Article  ADS  Google Scholar 

  6. Aubourg, É. et al. Cosmological implications of baryon acoustic oscillation measurements. Phys. Rev. D 92, 123516 (2015).

    Article  ADS  Google Scholar 

  7. Planck Collaboration et al. Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, A13 (2016).

    Article  Google Scholar 

  8. Raveri, M. Are cosmological data sets consistent with each other within the Λ cold dark matter model? Phys. Rev. D 93, 043522 (2016).

    Article  ADS  Google Scholar 

  9. Addison, G. E. et al. Quantifying discordance in the 2015 Planck CMB spectrum. Astrophys. J. 818, 132 (2016).

    Article  ADS  Google Scholar 

  10. Bernal, J. L., Verde, L. & Riess, A. G. The trouble with H 0. J. Cosmol. Astropart. Phys. 10, 019 (2016).

    Article  ADS  Google Scholar 

  11. Freedman, W. L. Cosmology at a crossroads. Nat. Astron. 1, 0121 (2017).

    Article  ADS  Google Scholar 

  12. Riess, A. G. et al. A 2.4% determination of the local value of the Hubble constant. Astrophys. J. 826, 56 (2016).

    Article  ADS  Google Scholar 

  13. Kullback, S. & Leibler, R. A. On information and sufficiency. Ann. Math. Stat. 22, 79 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  14. DESI Collaboration et al. The DESI experiment part I: science, targeting, and survey design. Preprint at https://arxiv.org/abs/1611.00036 (2016).

  15. Seehars, S., Amara, A., Refregier, A., Paranjape, A. & Akeret, J. Information gains from cosmic microwave background experiments. Phys. Rev. D 90, 023533 (2014).

    Article  ADS  Google Scholar 

  16. Linder, E. V. Exploring the expansion history of the Universe. Phys. Rev. Lett. 90, 091301 (2003).

    Article  ADS  Google Scholar 

  17. Crittenden, R. G., Zhao, G.-B., Pogosian, L., Samushia, L. & Zhang, X. Fables of reconstruction: controlling bias in the dark energy equation of state. J. Cosmol. Astropart. Phys. 2, 048 (2012).

    Article  ADS  Google Scholar 

  18. Vikman, A. Can dark energy evolve to the phantom? Phys. Rev. D 71, 023515 (2005).

    Article  ADS  Google Scholar 

  19. Feng, B., Wang, X. & Zhang, X. Dark energy constraints from the cosmic age and supernova. Phys. Lett. B 607, 35–41 (2005).

    Article  ADS  Google Scholar 

  20. Das, S., Corasaniti, P. S. & Khoury, J. Superacceleration as the signature of a dark sector interaction. Phys. Rev. D 73, 083509 (2006).

    Article  ADS  Google Scholar 

  21. Zhao, G.-B., Crittenden, R. G., Pogosian, L. & Zhang, X. Examining the evidence for dynamical dark energy. Phys. Rev. Lett. 109, 171301 (2012).

    Article  ADS  Google Scholar 

  22. Reid, B. A. et al. The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measurements of the growth of structure and expansion rate at z=0.57 from anisotropic clustering. Mon. Not. R. Astron. Soc. 426, 2719–2737 (2012).

    Article  ADS  Google Scholar 

  23. Zhao, G.-B. et al. The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in Fourier space. Mon. Not. R. Astron. Soc. 466, 762–779 (2017).

    Article  ADS  Google Scholar 

  24. Riess, A. G. et al. A redetermination of the Hubble constant with the Hubble Space Telescope from a differential distance ladder. Astrophys. J. 699, 539–563 (2009).

    Article  ADS  Google Scholar 

  25. Larson, D. et al. Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: power spectra and WMAP-derived parameters. Astrophys. J. Suppl. 192, 16 (2011).

    Article  ADS  Google Scholar 

  26. Astier, P., Guy, J., Pain, R. & Balland, C. Dark energy constraints from a space-based supernova survey. Astron. Astrophys. 525, A7 (2011).

    Article  ADS  Google Scholar 

  27. Di Valentino, E., Melchiorri, A. & Silk, J. Reconciling Planck with the local value of H 0 in extended parameter space. Phys. Lett. B 761, 242–246 (2016).

    Article  ADS  Google Scholar 

  28. Solà, J., Gómez-Valent, A. & de Cruz Pérez, J. First evidence of running cosmic vacuum: challenging the concordance model. Astrophys. J. 836, 43 (2017).

    Article  ADS  Google Scholar 

  29. Wang, Y., Zhao, G.-B., Wands, D., Pogosian, L. & Crittenden, R. G. Reconstruction of the dark matter–vacuum energy interaction. Phys. Rev. D 92, 103005 (2015).

    Article  ADS  Google Scholar 

  30. Bautista, J. E. et al. Measurement of BAO correlations at z=2.3 with SDSS DR12 Lyα-forests. Preprint at https://arxiv.org/abs/1702.00176 (2017).

  31. Grandis, S., Seehars, S., Refregier, A., Amara, A. & Nicola, A. Information gains from cosmological probes. J. Cosmol. Astropart. Phys. 5, 034 (2016).

    Article  ADS  Google Scholar 

  32. Seehars, S., Grandis, S., Amara, A. & Refregier, A. Quantifying concordance in cosmology. Phys. Rev. D 93, 103507 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  33. Raveri, M., Martinelli, M., Zhao, G. & Wang, Y. Information gain in cosmology: from the discovery of expansion to future surveys. Preprint at https://arxiv.org/abs/1606.06273 (2016).

  34. Paykari, P. & Jaffe, A. H. Sparsely sampling the sky: a Bayesian experimental design approach. Mon. Not. R. Astron. Soc. 433, 3523–3533 (2013).

    Article  ADS  Google Scholar 

  35. Kunz, M., Trotta, R. & Parkinson, D. R. Measuring the effective complexity of cosmological models. Phys. Rev. D 74, 023503 (2006).

    Article  ADS  Google Scholar 

  36. Amara, A. & Refregier, A. Model breaking measure for cosmological surveys. Phys. Rev. D 89, 083501 (2014).

    Article  ADS  Google Scholar 

  37. Verde, L., Protopapas, P. & Jimenez, R. The expansion rate of the intermediate universe in light of Planck. Phys. Dark Univ. 5, 307–314 (2014).

    Article  Google Scholar 

  38. Charnock, T., Battye, R. A. & Moss, A. Planck confronts large scale structure: methods to quantify discordance. Preprint at https://arxiv.org/abs/1703.05959 (2017).

  39. Betoule, M. et al. Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples. Astron. Astrophys. 568, A22 (2014).

    Article  Google Scholar 

  40. Beutler, F. et al. The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Mon. Not. R. Astron. Soc. 416, 3017–3032 (2011).

    Article  ADS  Google Scholar 

  41. Ross, A. J. et al. The clustering of the SDSS DR7 main galaxy sample - I. A 4 per cent distance measure at z=0.15. Mon. Not. R. Astron. Soc. 449, 835–847 (2015).

    Article  ADS  Google Scholar 

  42. Parkinson, D. et al. The WiggleZ Dark Energy Survey: final data release and cosmological results. Phys. Rev. D 86, 103518 (2012).

    Article  ADS  Google Scholar 

  43. Heymans, C. et al. CFHTLenS tomographic weak lensing cosmological parameter constraints: mitigating the impact of intrinsic galaxy alignments. Mon. Not. R. Astron. Soc 432, 2433–2453 (2013).

    Article  ADS  Google Scholar 

  44. Moresco, M. et al. A 6% measurement of the Hubble parameter at z∼0.45: direct evidence of the epoch of cosmic re-acceleration. J. Cosmol. Astropart. Phys. 5, 014 (2016).

    Article  ADS  Google Scholar 

  45. Alam, S. et al. The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample. Preprint at https://arxiv.org/abs/1607.03155 (2016).

  46. Dalal, N., Pen, U.-L. & Seljak, U. Large-scale BAO signatures of the smallest galaxies. J. Cosmol. Astropart. Phys. 11, 007 (2010).

    Article  ADS  Google Scholar 

  47. Beutler, F., Seljak, U. & Vlah, Z. Constraining the relative velocity effect using the Baryon Oscillation Spectroscopic Survey. Preprint at https://arxiv.org/abs/1612.04720 (2016).

  48. Slepian, Z. et al. Constraining the baryon–dark matter relative velocity with the large-scale 3-point correlation function of the SDSS BOSS DR12 CMASS galaxies. Preprint at https://arxiv.org/abs/1607.06098 (2016).

  49. Ma, C., Corasaniti, P.-S. & Bassett, B. A. Application of Bayesian graphs to SN Ia data analysis and compression. Mon. Not. R. Astron. Soc. 463, 1651–1665 (2016).

    Article  ADS  Google Scholar 

  50. Shafieloo, A., Clifton, T. & Ferreira, P. The crossing statistic: dealing with unknown errors in the dispersion of type Ia supernovae. J. Cosmol. Astropart. Phys. 8, 017 (2011).

    Article  ADS  Google Scholar 

  51. Crittenden, R. G., Pogosian, L. & Zhao, G.-B. Investigating dark energy experiments with principal components. J. Cosmol. Astropart. Phys. 12, 025 (2009).

    Article  ADS  Google Scholar 

  52. Lewis, A., Challinor, A. & Lasenby, A. Efficient computation of cosmic microwave background anisotropies in closed Friedmann–Robertson–Walker models. Astrophys. J. 538, 473–476 (2000).

    Article  ADS  Google Scholar 

  53. Zhao, G.-B., Xia, J.-Q., Li, M., Feng, B. & Zhang, X. Perturbations of the Quintom models of dark energy and the effects on observations. Phys. Rev. D 72, 123515 (2005).

    Article  ADS  Google Scholar 

  54. Handley, W. J., Hobson, M. P. & Lasenby, A. N. POLYCHORD: nested sampling for cosmology. Mon. Not. R. Astron. Soc. 450, L61–L65 (2015).

    Article  ADS  Google Scholar 

  55. Lewis, A. & Bridle, S. Cosmological parameters from CMB and other data: a Monte Carlo approach. Phys. Rev. D 66, 103511 (2002).

    Article  ADS  Google Scholar 

  56. Huterer, D. & Starkman, G. Parametrization of dark energy properties: a principal component approach. Phys. Rev. Lett. 90, 031301 (2003).

    Article  ADS  Google Scholar 

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Acknowledgements

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

Authors and Affiliations

  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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  1. Gong-Bo Zhao
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Contributions

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.

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Correspondence to Gong-Bo Zhao.

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Zhao, GB., Raveri, M., Pogosian, L. et al. Dynamical dark energy in light of the latest observations. Nat Astron 1, 627–632 (2017). https://doi.org/10.1038/s41550-017-0216-z

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