Cosmological model-independent test of $\Lambda$CDM with two-point diagnostic by the observational Hubble parameter data

Aiming at exploring the nature of dark energy (DE), we use forty-three observational Hubble parameter data (OHD) in the redshift range \(0 < z \leqslant 2.36\) to make a cosmological model-independent test of the \(\varLambda \)CDM model with two-point \(Omh^2(z_{2};z_{1})\) diagnostic. In \(\varLambda \)CDM model, with equation of state (EoS) \(w=-1\), two-point diagnostic relation \(Omh^2 \equiv \varOmega _{\mathrm{m}}h^2\) is tenable, where \(\varOmega _{\mathrm{m}}\) is the present matter density parameter, and h is the Hubble parameter divided by 100 \({\mathrm {km\, s^{-1} \ Mpc^{-1}}}\). We utilize two methods: the weighted mean and median statistics to bin the OHD to increase the signal-to-noise ratio of the measurements. The binning methods turn out to be promising and considered to be robust. By applying the two-point diagnostic to the binned data, we find that although the best-fit values of \(Omh^2\) fluctuate as the continuous redshift intervals change, on average, they are continuous with being constant within 1 \(\sigma \) confidence interval. Therefore, we conclude that the \(\varLambda \)CDM model cannot be ruled out.