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

TL;DR

This paper demonstrates how current and future direct measurements of the Hubble parameter $H(z)$, including redshift-drift observations, can significantly improve constraints on dark energy models like $mbda$CDM, $w$CDM, CPL, and HDE.

Contribution

It analyzes the impact of current $H(z)$ data and future redshift-drift observations on constraining various dark energy models.

Findings

Current $H(z)$ measurements already constrain dark energy models.

Future redshift-drift data can extend $H(z)$ measurements to higher redshifts.

Redshift-drift observations can greatly improve dark energy constraints within 10 years.

Abstract

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, 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, $w$CDM, CPL, and holographic dark energy (HDE) models, can be constrained by the current direct measurements of $H(z)$ (31 data in total, 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.