## Abstract

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(z_{i}, z_{j}) and Omh^{2}(z_{i}, z_{j}), 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(z_{i}, z_{j}), 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 R_{h} = 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(z_{i}, z_{j}) diagnostics.

Original language | English (US) |
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Article number | stx1437 |

Pages (from-to) | 2320-2327 |

Number of pages | 8 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 470 |

Issue number | 2 |

DOIs | |

State | Published - Sep 11 2017 |

## Keywords

- 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