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.