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In the near future, the redshift drift observations in optical and radiobands will provide precise measurements on $H(z)$ covering the redshift rangesof $2<z<5$ and $0<z<0.3$. In addition, gravitational wave (GW) standard sirenobservations could make measurements on the dipole anisotropy of luminositydistance, which will also provide the $H(z)$ measurements in the redshift rangeof $0<z<3$. In this work, we propose a multi-messenger and multi-wavelengthobservational strategy to measure $H(z)$ based on the three next-generationprojects, E-ELT, SKA, and DECIGO, and we wish to see whether the future $H(z)$measurements could provide tight constraints on dark-energy parameters. Thedark energy models we consider include $\Lambda$CDM, $w$CDM, CPL, HDE, andI$\Lambda$CDM models. It is found that E-ELT, SKA1, and DECIGO are highlycomplementary in constraining dark energy models. Although any one of thesethree data sets can only give rather weak constraints on each model weconsider, the combination of them could significantly break the parameterdegeneracies and give much tighter constraints on almost all the cosmologicalparameters. Moreover, we find that the combination of E-ELT, SKA1, DECIGO, andCMB could further improve the constraints on dark energy parameters, e.g.,$\sigma(w_0)=0.024$ and $\sigma(w_a)=0.17$ in the CPL model, which means thatthese three promising probes will play a key role in helping reveal the natureof dark energy.

journal of cosmology and astroparticle physics

Using a multi-messenger and multi-wavelength observational strategy to  probe the nature of dark energy through direct measurements of cosmic  expansion history