Using simulated Tianqin gravitational wave data and electromagnetic wave data to study the coincidence problem and Hubble tension problem

In this paper, we use electromagnetic wave data (H0LiCOW, $H(z)$, SNe) and gravitational wave data (Tianqin) to constrain the interacting dark energy (IDE) model and investigate the Hubble tension problem and coincidences problem. By combining these four kinds of data (Tianqin+H0LiCOW+SNe+$H(z)$), we obtained the parameter values at the confidence interval of $1\sigma$: $\Omega_m=0.36\pm0.18$, $\omega_x=-1.29^{+0.61}_{-0.23}$, $\xi=3.15^{+0.36}_{-1.1}$, and $H_0=70.04\pm0.42$ $kms^{-1}Mpc^{-1}$. According to our results, the best valve of $H_0$ show that the Hubble tension problem can be alleviated to some extent. In addition, the $\xi+3\omega_x = -0.72^{+2.19}_{-1.19}(1\sigma)$ of which the center value indicates the coincidence problem is slightly alleviated. However, the $\xi+3\omega_x = 0$ is still within the $1\sigma$ error range which indicates the $\Lambda$CDM model is still the model which is in best agreement with the observational data at present. Finally, we compare the constraint results of electromagnetic wave and gravitational wave on the model parameters and find that the constraint effect of electromagnetic wave data on model parameters is better than that of simulated Tianqin gravitational wave data.