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Detection of the cosmological time dilation of high-redshift quasars


A fundamental prediction of relativistic cosmologies is that, owing to the expansion of space, observations of the distant cosmos should be time dilated and appear to run slower than events in the local universe. While observations of cosmological supernovae unambiguously show the expected redshift-dependent time dilation, this has not been the case for other distant sources. Here we present the identification of cosmic time dilation in a sample of 190 quasars monitored for over two decades in multiple wavebands by assessing various hypotheses through Bayesian analysis. This detection counters previous claims that observed quasar variability lacked the expected redshift-dependent time dilation. Hence, as well as dismissing the claim that the apparent lack of the redshift dependence of quasar variability represents a substantial challenge to the standard cosmological model, this analysis further indicates that the properties of quasars are consistent with them being truly cosmologically distant sources.

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Fig. 1: Posterior distribution of the redshift dependence for the time dilation.
Fig. 2: Quasar subsamples as a function of rest wavelength and bolometric luminosity.
Fig. 3: Posterior distributions for the normalization parameters.

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Data availability

The source data for this project are available at, with the details of the available FITS tables presented in ref. 27. Note that a revised version of this catalogue was recently released due to an error in some rest-frame quantities. This revision does not impact any of the research presented in this paper. The software for this project is available at

Code availability

This project made use of several publicly available software packages, especially DNest436 to undertake the exploration of the posterior probability space and calculate the Bayesian evidence by integrating across this space. Further software packages employed include matplotlib39, numpy40 and scipy41. Initial explorations of the posterior probability space were undertaken with emcee with corner plots prepared with corner42. The software employed as part of this project will be made available on reasonable request to the corresponding author.


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We thank Z. Stone et al.27 for making their data and the results of their analysis publicly available. We also thank S. Croom for his input and advice on quasar variability surveys. We further thank the teams responsible for creating and maintaining the various software packages, detailed below, that this study has employed. G.F.L. thanks the hospitality of the Lowell Observatory where the last stages of this work were completed during a period of isolation due to the contraction of COVID-19.

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Authors and Affiliations



The project was conceived by G.F.L., including an initial exploration of the data, the definition of the models and hypotheses considered, the likelihood function and sampling of the posterior space. B.J.B. undertook detailed sampling and calculating the Bayesian evidence using DNest4. Both authors discussed the results of the exploration in detail, determined the resulting conclusion and were responsible for the writing of the paper.

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Correspondence to Geraint F. Lewis.

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Nature Astronomy thanks Deborah Dultzin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Lewis, G.F., Brewer, B.J. Detection of the cosmological time dilation of high-redshift quasars. Nat Astron 7, 1265–1269 (2023).

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