Constraining dark energy with Hubble parameter measurements: an analysis including future redshift-drift observations

The nature of dark energy affects the Hubble expansion rate (namely, the expansion history) H(z) by an integral over w(z). However, the usual observables are the luminosity distances or the angular diameter distances, which measure the distance–redshift relation. Actually, the property of dark energy affects the distances (and the growth factor) by a further integration over functions of H(z). Thus, the direct measurements of the Hubble parameter H(z) at different redshifts are of great importance for constraining the properties of dark energy. In this paper, we show how the typical dark energy models, for example, the $$\Lambda $$ CDM, wCDM, CPL, and holographic dark energy models, can be constrained by the current direct measurements of H(z) (31 data used in total in this paper, covering the redshift range of $$z\in [0.07,2.34]$$ ). In fact, the future redshift-drift observations (also referred to as the Sandage–Loeb test) can also directly measure H(z) at higher redshifts, covering the range of $$z\in [2,5]$$ . We thus discuss what role the redshift-drift observations can play in constraining dark energy with the Hubble parameter measurements. We show that the constraints on dark energy can be improved greatly with the H(z) data from only a 10-year observation of redshift drift.