Using a multi-messenger and multi-wavelength observational strategy to
  probe the nature of dark energy through direct measurements of cosmic
  expansion history
  In the near future, the redshift drift observations in optical and radio
bands will provide precise measurements on $H(z)$ covering the redshift ranges
of $2<z<5$ and $0<z<0.3$. In addition, gravitational wave (GW) standard siren
observations could make measurements on the dipole anisotropy of luminosity
distance, which will also provide the $H(z)$ measurements in the redshift range
of $0<z<3$. In this work, we propose a multi-messenger and multi-wavelength
observational strategy to measure $H(z)$ based on the three next-generation
projects, E-ELT, SKA, and DECIGO, and we wish to see whether the future $H(z)$
measurements could provide tight constraints on dark-energy parameters. The
dark energy models we consider include $\Lambda$CDM, $w$CDM, CPL, HDE, and
I$\Lambda$CDM models. It is found that E-ELT, SKA1, and DECIGO are highly
complementary in constraining dark energy models. Although any one of these
three data sets can only give rather weak constraints on each model we
consider, the combination of them could significantly break the parameter
degeneracies and give much tighter constraints on almost all the cosmological
parameters. Moreover, we find that the combination of E-ELT, SKA1, DECIGO, and
CMB 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 that
these three promising probes will play a key role in helping reveal the nature
of dark energy.
