Analysing H(z) data using two-point diagnostics

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 Omh²(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.