Utility of observational Hubble parameter data on dark energy evolution

Aiming at exploring the nature of dark energy, we use thirty-six observational Hubble parameter data (OHD) in the redshift range $0 \leqslant z \leqslant 2.36$tomakeacosmologicalmodel-independenttestofthetwo-point$Omh^2(z_{2};z_{1})$diagnostic\mathrm{.}In$\Lambda$CDM,wehave$Omh^2 \equiv \Omega_{m}h^2$,where$\Omega_{m}$ is the matter density parameter at present. We bin all the OHD into four data points to mitigate the observational contaminations. By comparing with the value of ${\mathrm{\Omega }}_m{h}^2$ which is constrained tightly by the Planck observations, our results show that in all six testing pairs of $Om{h}^2$ there are two testing pairs are consistent with $\mathrm{\Lambda }$CDM at $1\sigma$ confidence level (CL), whereas for another two of them $\mathrm{\Lambda }$CDM can only be accommodated at $2\sigma$ CL. Particularly, for remaining two pairs, $\mathrm{\Lambda }$CDM is not compatible even at $2\sigma$ CL. Therefore it is reasonable that although deviations from $\mathrm{\Lambda }$CDM exist for some pairs, cautiously, we cannot rule out the validity of $\mathrm{\Lambda }$CDM. We further apply two methods to derive the value of Hubble constant $H_0$ utilizing the two-point $Om{h}^2(z_2;z_1)$ diagnostic. We obtain $H_0 = 71.23\pm1.54$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$ from inverse variance weighted $Om{h}^2$ value (method (I)) and $H_0=69.37\pm 1.59$ ${\mathrm{km
s^{-1} \ Mpc^{-1}}}$thatthe$Omh^2$ value originates from Planck measurement (method (II)), both at $1\sigma$ CL. Finally, we explore how the error in OHD propagate into $w(z)$ at certain redshift during the reconstruction of $w(z)$. We argue that the current precision on OHD is not sufficient small to ensure the reconstruction of $w(z)$ in an acceptable error range, especially at the low redshift