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 forthcoming decades, the redshift drift observations in optical and radio bands will provide accurate measurements on $H(z)$ covering the redshift ranges of $2<z<5$ and $0<z<1$. 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. It is found that E-ELT, SKA1, and DECIGO are highly complementary in constraining dark energy models using the $H(z)$ data. We find that E-ELT, SKA1, and DECIGO can tightly constrain $Omega_m$, $w$ (or $w_0$), and $H_0$, respectively, and thus the combination of them could effectively break the cosmological parameter degeneracies. The joint E-ELT+SKA1+DECIGO data give $sigma(w)approx 0.02$ in the $w$CDM model and $sigma(w_0)approx 0.03$ in the CPL model, which are better than the results of {it Planck} 2018 TT,TE,EE+lowE+lensing+SNe+BAO. But even the joint data cannot well constrain $w_a$ in the CPL model.