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

We investigate whether the current Hubble parameter $H(z)$ measurements could help improve the constraints on dark energy on the basis of the mainstream cosmological probes including the type Ia supernovae (SN) observation, the cosmic microwave background anisotropies (CMB) observation, and the baryon acoustic oscillations (BAO) observation. For the current $H(z)$ data, we use 30 data points measured by using a differential age method. Furthermore, we also consider the future $H(z)$ measurements based on the Sandage-Loeb (SL) test by means 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 four typical 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 the analysis. We find that, when only the current $H(z)$ data are added, the constraints on these models are not improved compared to the cases using the SN+CMB+BAO data; but when further adding the 10-year SL test data, the constraint results are tremendously improved for all the four models. Therefore, we conclude that, although the current $H(z)$ measurements could not provide an evident improvement on the basis of the current mainstream cosmological probes, the future $H(z)$ measurements from the SL test would have enormous potential to change the status of the Hubble parameter measurements in constraining dark energy.