Statistical analysis with cosmic-expansion-rate measurements and two-point diagnostics

Direct measurements of Hubble parameters $H(z)$ are very useful for cosmological model parameters inference. Based on them, Sahni, Shafieloo and Starobinski introduced a two-point diagnostic $Omh^2(z_i, z_j)$ as an interesting tool for testing the validity of the $\Lambda$CDM model. Applying this test they found a tension between observations and predictions of the $\Lambda$CDM model. We use the most comprehensive compilation $H(z)$ data from baryon acoustic oscillations (BAO) and differential ages (DA) of passively evolving galaxies to study cosmological models using the Hubble parameters itself and to distinguish whether $\Lambda$CDM model is consistent with the observational data with statistical analysis of the corresponding $Omh^2(z_i, z_j)$ two-point diagnostics. Our results show that presently available $H(z)$ data significantly improve the constraints on cosmological parameters. The corresponding statistical $Omh^2(z_i, z_j)$ two-point diagnostics seems to prefer the quintessence with $w>-1$ over the $\Lambda$CDM model. Better and more accurate prior knowledge of the Hubble constant, will considerably improve the performance of the statistical $Omh^2(z_i, z_j)$ method.