# Analyzing H(z) Data using Two-point Diagnostics

## TL;DR

This paper refines 2-point diagnostics for H(z) data, focusing on model-independent cosmic chronometer measurements, revealing that most cosmological models remain consistent with data except Einstein-de Sitter, which is strongly ruled out.

## Contribution

It introduces new variations of 2-point diagnostics, specifically Delta h(z_i,z_j), and emphasizes the importance of using model-independent data and appropriate statistical methods.

## Key findings

- Most models, including LCDM, are consistent within 1 sigma with the data.
- Einstein-de Sitter is ruled out at over 3 sigma significance.
- Previous analyses underestimated errors, affecting tension assessments.

## Abstract

Measurements of the Hubble constant H(z) are increasingly being used to test the expansion rate predicted by various cosmological models. But the recent application of 2-point diagnostics, such as Om(z_i,z_j) and Omh^2(z_i,z_j), has produced considerable tension between LCDM'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-chronomter approach, and model-dependent data extracted from BAOs. In this paper, we advance the use of 2-point diagnostics beyond their current status, and introduce new variations, which we call Delta h(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 2-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 2-point diagnostics at a level of significance exceeding ~ 3 sigma. The R_h=ct universe is slightly favoured over the remaining models, including LCDM and Chevalier-Polarski-Linder, though all of them (other than Einstein-de Sitter) are consistent to within 1 sigma with the measured mean of the Delta h(z_i,z_j) diagnostics.