Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Cosmological constraints from the Hubble diagram of quasars at high redshifts


The concordance model (Λ cold dark matter (ΛCDM) model, where Λ is the cosmological constant) reproduces the main current cosmological observations1,2,3,4 assuming the validity of general relativity at all scales and epochs and the presence of CDM and of Λ, equivalent to dark energy with a constant density in space and time. However, the ΛCDM model is poorly tested in the redshift interval between the farthest observed type Ia supernovae5 and the cosmic microwave background. We present measurements of the expansion rate of the Universe based on a Hubble diagram of quasars. Quasars are the most luminous persistent sources in the Universe, observed up to redshifts of z ≈ 7.5 (refs. 6,7). We estimate their distances following a method developed by our group8,9,10, based on the X-ray and ultraviolet emission of the quasars. The distance modulus/redshift relation of quasars at z < 1.4 is in agreement with that of supernovae and with the concordance model. However, a deviation from the ΛCDM model emerges at higher redshift, with a statistical significance of ~4σ. If an evolution of the dark energy equation of state is allowed, the data suggest dark energy density increasing with time.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Relation between the UV and X-ray monochromatic luminosities of quasars.
Fig. 2: Hubble diagram of type Ia supernovae and quasars.
Fig. 3: Test of the ΛCDM model through a cosmographic expansion.
Fig. 4: Error contours for an evolving dark energy model.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

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

  2. 2.

    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 

  3. 3.

    Aubourg, E. et al. Cosmological implications of baryon acoustic oscillation measurements. Phys. Rev. D 22, 123516 (2015).

    ADS  Article  Google Scholar 

  4. 4.

    Mantz, A. B. et al. Cosmology and astrophysics from relaxed galaxy clusters. II. Cosmological constraints. Mon. Not. R. Astron. Soc. 440, 2077–2098 (2014).

    ADS  Article  Google Scholar 

  5. 5.

    Suzuki, N. et al. The Hubble Space Telescope Cluster Supernova Survey. V. Improving the dark-energy constraints above z > 1 and building an early-type-hosted supernova sample. Astrophys. J. 746, 85 (2012).

    ADS  Article  Google Scholar 

  6. 6.

    Mortlock, D. J. et al. A luminous quasar at a redshift of z = 7.085. Nature 474, 616–619 (2011).

    ADS  Article  Google Scholar 

  7. 7.

    Bañados, E. et al. An 800-million-solar-mass black hole in a significantly neutral Universe at a redshift of 7.5. Nature 553, 473–476 (2018).

    ADS  Article  Google Scholar 

  8. 8.

    Risaliti, G. & Lusso, E. A Hubble diagram for quasars. Astrophys. J. 815, 33 (2015).

    ADS  Article  Google Scholar 

  9. 9.

    Lusso, E. & Risaliti, G. The tight relation between X-ray and ultraviolet luminosity of quasars. Astrophys. J. 819, 154 (2016).

    ADS  Article  Google Scholar 

  10. 10.

    Lusso, E. & Risaliti, G. Quasars as standard candles. I. The physical relation between disc and coronal emission. Astron. Astrophys. 602, A79 (2017).

    ADS  Article  Google Scholar 

  11. 11.

    Shakura, N. I. & Sunyaev, R. A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973).

    ADS  Google Scholar 

  12. 12.

    Avni, Y. & Tananbaum, H. X-ray properties of optically selected QSOs. Astrophys. J. 305, 83–99 (1986).

    ADS  Article  Google Scholar 

  13. 13.

    Just, D. W. et al. The X-ray properties of the most luminous quasars from the Sloan Digital Sky Survey. Astrophys. J. 665, 1004–1022 (2007).

    ADS  Article  Google Scholar 

  14. 14.

    Lusso, E. et al. The X-ray to optical-UV luminosity ratio of X-ray selected type 1 AGN in XMM-COSMOS. Astron. Astrophys. 512, A34 (2010).

    Article  Google Scholar 

  15. 15.

    Young, M., Risaliti, G. & Elvis, M. The X-ray energy dependence of the relation between optical and X-ray emission in quasars. Astrophys. J. 708, 1388–1397 (2010).

    ADS  Article  Google Scholar 

  16. 16.

    Jansen, F. et al. XMM-Newton observatory. I. The spacecraft and operations. Astron. Astrophys. 365, L1–L6 (2001).

    ADS  Article  Google Scholar 

  17. 17.

    Rosen, S. R. et al. The XMM-Newton serendipitous survey. VII. The third XMM-Newton serendipitous source catalogue. Astron. Astrophys. 590, A1 (2016).

    Article  Google Scholar 

  18. 18.

    Shen, Y. et al. A catalog of quasar properties from Sloan Digital Sky Survey data release 7. Astrophys. J. Suppl. S. 194, 45 (2011).

    ADS  Article  Google Scholar 

  19. 19.

    Paris, I. et al. The Sloan Digital Sky Survey quasar catalog: twelfth data release. Astron. Astrophys. 597, A79 (2017).

    Article  Google Scholar 

  20. 20.

    Kalfountzou, E. et al. The largest X-ray-selected sample of z > 3 AGNs: C-COSMOS and ChaMP. Mon. Not. R. Astron. Soc. 445, 1430–1448 (2014).

    ADS  Article  Google Scholar 

  21. 21.

    Vagnetti, F., Antonucci, M. & Trevese, D. Variability and the X-ray/UV ratio of active galactic nuclei. II. Analysis of a low-redshift Swift sample. Astron. Astrophys. 550, A71 (2013).

    ADS  Article  Google Scholar 

  22. 22.

    Brusa, M. et al. The XMM-Newton wide-field survey in the COSMOS field (XMM-COSMOS): demography and multiwavelength properties of obscured and unobscured luminous active galactic nuclei. Astrophys. J. 716, 348–369 (2010).

    ADS  Article  Google Scholar 

  23. 23.

    Paolillo, M. et al. Tracing the accretion history of supermassive black holes through X-ray variability: results from the ChandraDeep Field-South. Mon. Not. R. Astron. Soc. 471, 4398–4411 (2017).

    ADS  Article  Google Scholar 

  24. 24.

    MacLeod, C. et al. A description of quasar variability measured using repeated SDSS and POSS imaging. Astrophys. J. 753, 106 (2012).

    ADS  Article  Google Scholar 

  25. 25.

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

    ADS  Article  Google Scholar 

  26. 26.

    Planck Collaboration et al. Planck 2015 results. XIV. Dark energy and modified gravity. Astron. Astrophys. 594, A14 (2016).

  27. 27.

    Riess, A. G. et al. Type Ia supernova distances at redshift >1.5 from the Hubble Space Telescope Multi-cycle Treasury programs: the early expansion rate. Astrophys. J. 853, 126 (2018).

    ADS  Article  Google Scholar 

  28. 28.

    Gibson, R. R., Brandt, W. N., Gallagher, S. C. & Schneider, D. P. A catalog of broad absorption line quasars in Sloan Digital Sky Survey data release 5. Astrophys. J. 692, 758–777 (2009).

    ADS  Article  Google Scholar 

  29. 29.

    Mingo, B. et al. The MIXR sample: AGN activity versus star formation across the cross-correlation of WISE, 3XMM, and FIRST/NVSS. Mon. Not. R. Astron. Soc. 462, 2631–2667 (2016).

    ADS  Article  Google Scholar 

  30. 30.

    Hasinger, G. et al. The XMM-Newton wide-field survey in the COSMOS field. I. Survey description. Astrophys. J. Suppl. S. 172, 29–37 (2007).

    ADS  Article  Google Scholar 

  31. 31.

    Cappelluti, N. et al. The XMM-Newton wide-field survey in the COSMOS field. The point-like X-ray source catalogue. Astron. Astrophys. 497, 635–648 (2009).

    ADS  Article  Google Scholar 

  32. 32.

    Nanni, R., Vignali, C., Gilli, R., Moretti, A. & Brandt, W. N. The X-ray properties of z ~ 6 luminous quasars. Astron. Astrophys. 603, A128 (2017).

    ADS  Article  Google Scholar 

  33. 33.

    Green, P. J. et al. The soft X-ray properties of a large optical QSO sample: ROSAT observations of the Large Bright Quasar Survey. Astrophys. J. 450, 51 (1995).

    ADS  Article  Google Scholar 

  34. 34.

    Gallagher, S. C., Brandt, W. N., Sambruna, R. M., Mathur, S. & Yamasaki, N. Exploratory ASCA observations of broad absorption line quasi-stellar objects. Astrophys. J. 519, 549–555 (1999).

    ADS  Article  Google Scholar 

  35. 35.

    Brandt, W. N., Laor, A. & Wills, B. J. On the nature of soft X-ray weak quasi-stellar objects. Astrophys. J. 528, 649 (2000).

    Article  Google Scholar 

  36. 36.

    Hewett, P. C. & Foltz, C. B. The frequency and radio properties of broad absorption line quasars. Astron. J. 125, 1784–1794 (2003).

    ADS  Article  Google Scholar 

  37. 37.

    Richards, G. T. et al. Red and reddened quasars in the Sloan Digital Sky Survey. Astron. J. 126, 1131–1147 (2003).

    ADS  Article  Google Scholar 

  38. 38.

    Merloni, A. et al. The incidence of obscuration in active galactic nuclei. Mon. Not. R. Astron. Soc. 437, 3550–3567 (2014).

    ADS  Article  Google Scholar 

  39. 39.

    Bianchi, S. et al. CAIXA: a catalogue of AGN in the XMM-Newton archive. I. Spectral analysis. Astron. Astrophys. 495, 421–430 (2009).

    ADS  Article  Google Scholar 

  40. 40.

    Prevot, M. L., Lequeux, J., Maurice, E., Prevot, L. & Rocca-Volmerange, B. The typical interstellar extinction in the Small Magellanic Cloud. Astron. Astrophys. 132, 389–392 (1984).

    ADS  Google Scholar 

  41. 41.

    Watson, M. G. et al. The XMM-Newton Serendipitous Survey. I. The role of XMM-Newton Survey Science Centre. Astron. Astrophys. 365, L51–L59 (2001).

    ADS  Article  Google Scholar 

  42. 42.

    Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 126, 306 (2013).

    ADS  Article  Google Scholar 

  43. 43.

    Kelly, B. C. Some aspects of measurement error in linear regression of astronomical data. Astrophys. J. 665, 1489–1506 (2007).

    ADS  Article  Google Scholar 

  44. 44.

    Zheng, W., Kriss, G. A., Telfer, R. C., Grimes, J. P. & Davidsen, A. F. A composite HST spectrum of quasars. Astrophys. J. 475, 469–478 (1997).

    ADS  Article  Google Scholar 

  45. 45.

    Lusso, E. et al. The first ultraviolet quasar-stacked spectrum at z ~ 2.4 from WFC3. Mon. Not. R. Astron. Soc. 449, 4204–4220 (2015).

    ADS  Article  Google Scholar 

  46. 46.

    Tilton, E. M., Stevans, M. L., Shull, J. M. & Danforth, C. W. HST-COS observations of AGNs. III. Spectral constraints in the Lyman continuum from composite COS/G140L data. Astrophys. J. 817, 56 (2016).

    ADS  Article  Google Scholar 

  47. 47.

    Shull, J. M., Danforth, C. W., Tilton, E. M., Moloney, J. & Stevans, M. L. An ultraviolet survey of low-redshift partial Lyman-limit systems with the HST Cosmic Origins Spectrograph. Astrophys. J. 849, 106 (2017).

    ADS  Article  Google Scholar 

  48. 48.

    Stevans, M. L., Shull, J. M., Danforth, C. W. & Tilton, E. M. HST-COS observations of AGNs. II. Extended survey of ultraviolet composite spectra from 159 active galactic nuclei. Astrophys. J. 794, 75 (2014).

    ADS  Article  Google Scholar 

Download references


We are grateful to our collaborators S. Bisogni, M. Elvis, R. Gilli, E. Nardini, M. Salvati, F. Salvestrini and C. Vignali for discussions and comments on the main topics of this work. G.R. acknowledges the support of grant ASI-INAF no. 2017–14-H.0. E.L. is supported by a European Union COFUND/Durham Junior Research Fellowship (under EU grant agreement no. 609412). This work has made use of data from the SDSS, SDSS-II and SDSS-III surveys, of the 3XMM Source Catalog and of XMM-Newton and Chandra observations. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the United States Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society and the Higher Education Funding Council for England. The SDSS website is The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max Planck Institute for Astronomy (MPIA), the Max Planck Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory and the University of Washington. 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 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 Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, the Max Planck Institute for Astrophysics, the 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




Both authors contributed equally to the scientific content and the writing of this paper.

Corresponding author

Correspondence to G. Risaliti.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Text, Supplementary Figures 1–17, Supplementary References 1–38

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Risaliti, G., Lusso, E. Cosmological constraints from the Hubble diagram of quasars at high redshifts. Nat Astron 3, 272–277 (2019).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing