Observational constraints and diagnostics for time-dependent dark energy models

In this paper, we constrain four time-dependent dark energy (TDDE) models by using the Type Ia supernovae (SNe Ia), baryonic acoustic oscillations (BAO), observational Hubble parameter (OHD) data-sets as well as the single data point from the newest event GW150914. Subsequently, adopting the best fitting values of the model parameters, we apply the original statefinder, statefinder hierarchy, the growth rate of matter perturbations and $Om(z)$ diagnostics to distinguish the TDDE scenarios and the $\Lambda$CDM scenario from each other. We discover that all the TDDE models and $\Lambda$CDM model can be distinguished better at the present epoch by using the statefinder hierarchy than using the original statefinder, the growth rate of matter perturbations and $Om(z)$ diagnostics, especially, in the planes of $\{S_3^{(1)},S_4^{(1)}\}$, $\{S_3^{(2)},S_4^{(2)}\}$, $\{S_5^{(1)},S_5^{(2)}\}$ and $\{S_4^{(2)},S_5^{(2)}\}$.