Investigating the dynamical models of cosmology with recent observations
  and upcoming gravitational-wave data
  We explore and compare the capabilities of the recent observations of
standard cosmological probes and the future observations of gravitational-wave
(GW) standard sirens on constraining cosmological parameters. It is carried out
in the frameworks of two typical dynamical models of cosmology, i.e., the
$\omega_0\omega_a$CDM model with $\omega(z) = \omega_0 +\omega_a*z/(1+z)$, and
the $\xi$-index model with $\rho_X\propto\rho_ma^{\xi}$, where $\omega(z)$ is
the dark energy equation of state, and $\rho_X$ and $\rho_m$ are the energy
densities of dark energy and matter, respectively. In the cosmological
analysis, the employed data sets include the recent observations of the
standard cosmological probes, i.e., Type Ia supernovae (SNe Ia), baryon
acoustic oscillation (BAO) and cosmic microwave background (CMB), and also the
mock GW standard siren sample with 1000 merging neutron star events anticipated
from the third-generation detectors. In the scenarios of both
$\omega_0\omega_a$CDM and $\xi$-index models, it turns out that the mock GW
sample can reduce the uncertainty of the Hubble constant $H_0$ by about 50\%
relative to that from the joint SNe+BAO+CMB sample; nevertheless, the
SNe+BAO+CMB sample demonstrates better performance on limiting other
parameters. Furthermore, the Bayesian evidence is applied to compare the
dynamical models with the $\Lambda$CDM model. The Bayesian evidences computed
from the SNe+BAO+CMB sample reveal that the $\Lambda$CDM model is the most
supported one; moreover, the $\omega_0\omega_a$CDM model is more competitive
than the $\xi$-index model.
