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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 $ω_0ω_a$CDM model with $ω(z) = ω_0 +ω_a*z/(1+z)$, and the $ξ$-index model with $ρ_X\proptoρ_ma^ξ$, where $ω(z)$ is the dark energy equation of state, and $ρ_X$ and $ρ_m$ 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 $ω_0ω_a$CDM and $ξ$-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 $Λ$CDM model. The Bayesian evidences computed from the SNe+BAO+CMB sample reveal that the $Λ$CDM model is the most supported one; moreover, the $ω_0ω_a$CDM model is more competitive than the $ξ$-index model.