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We investigate whether the current Hubble parameter $H(z)$ measurements couldhelp improve the constraints on dark energy on the basis of the mainstreamcosmological probes including the type Ia supernovae (SN) observation, thecosmic microwave background anisotropies (CMB) observation, and the baryonacoustic oscillations (BAO) observation. For the current $H(z)$ data, we use 30data points measured by using a differential age method. Furthermore, we alsoconsider the future $H(z)$ measurements based on the Sandage-Loeb (SL) test bymeans of the E-ELT in construction, and thus we also use 30 simulated $H(z)$data according to a 10-year SL test observation. In this work, we choose fourtypical dark energy models as examples, i.e., the $\Lambda$CDM model, the$w$CDM model, the $\alpha$DE model, and the GCG model, to complete theanalysis. We find that, when only the current $H(z)$ data are added, theconstraints on these models are not improved compared to the cases using theSN+CMB+BAO data; but when further adding the 10-year SL test data, theconstraint results are tremendously improved for all the four models.Therefore, we conclude that, although the current $H(z)$ measurements could notprovide an evident improvement on the basis of the current mainstreamcosmological probes, the future $H(z)$ measurements from the SL test would haveenormous potential to change the status of the Hubble parameter measurements inconstraining dark energy.

Revisit of constraints on dark energy with Hubble parameter measurements including future redshift drift observations