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 $$\Lambda \hbox {CDM}$$ model. Applying this test they found a tension between observations and predictions of the $$\Lambda \hbox {CDM}$$ 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 $$\Lambda \hbox {CDM}$$ 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 $$\Lambda \hbox {CDM}$$ 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