Analysing H(z) data using two-point diagnostics

Kyle Leaf, Fulvio Melia

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Measurements of the Hubble constantH(z) are increasingly being used to test the expansion rate predicted by various cosmological models. But the recent application of two-point diagnostics, such as Om(zi, zj) and Omh2(zi, zj), has produced considerable tension between ΛCDM's predictions and several observations, with other models faring even worse. Part of this problem is attributable to the continued mixing of truly model-independent measurements using the cosmic-chronometer approach, and model-dependent data extracted from baryon acoustic oscillations. In this paper, we advance the use of two-point diagnostics beyond their current status, and introduce new variations, which we call Δh(zi, zj), that are more useful for model comparisons. But we restrict our analysis exclusively to cosmic-chronometer data, which are truly model independent. Even for these measurements, however, we confirm the conclusions drawn by earlier workers that the data have strongly non-Gaussian uncertainties, requiring the use of both 'median' and 'mean' statistical approaches. Our results reveal that previous analyses using two-point diagnostics greatly underestimated the errors, thereby misinterpreting the level of tension between theoretical predictions and H(z) data. Instead, we demonstrate that as of today, only Einstein-de Sitter is ruled out by the two-point diagnostics at a level of significance exceeding ~3σ. The Rh = ct universe is slightly favoured over the remaining models, including Lambda cold dark matter and Chevalier-Polarski-Linder, though all of them (other than Einstein-de Sitter) are consistent to within 1σ with the measured mean of the Δh(zi, zj) diagnostics.

Original languageEnglish (US)
Pages (from-to)2320-2327
Number of pages8
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
StatePublished - Sep 11 2017


  • Cosmology: observations
  • Cosmology: theory
  • Galaxies: distances and redshifts
  • Galaxies: evolution
  • Large-scale structure of Universe

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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