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

Rui-Yun Guo,Xin Zhang

doi:10.1140/epjc/s10052-016-4016-x

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.

Highlights

Is valid on all scales of the universe, the fact of cosmic acceleration implies that a new energy component with negative pressure, referred to as “dark energy” [7,8,9,10,11,12,13,14,15,16], is needed in the universe
The direct measurements of the Hubble parameter at different redshifts are vitally important for constraining the property of dark energy
The constraints on dark energy are often provided by the distance-redshift relation measurements, but the distance is linked to dark energy by an integral over 1/H (z), and H (z) is affected by dark energy via another integral over w(z)

Summary

Introduction

Is valid on all scales of the universe, the fact of cosmic acceleration implies that a new energy component with negative pressure, referred to as “dark energy” [7,8,9,10,11,12,13,14,15,16], is needed in the universe. A basic strategy is to accurately measure the both histories of cosmic expansion and growth of structure and to compare them for a consistency check. Dark energy affects the expansion history and growth of structure of the universe in a subtle way. To measure the history of the cosmic expansion, the most important way is to measure the distance–redshift relation. The cosmic distance, whether the luminosity distance or the angular diameter distance, is linked to the Hubble expansion rate. The property of dark energy affects the Hubble expansion rate H (z) through an integral, namely, in a flat universe, we have. J. C (2016) 76:163 where r and m are the current density parameters of radiation and matter, respectively, and X (z) describes how dark energy density evolves with redshift, z 1 + w(z )

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Conclusion