Exploring the potentiality of future standard candles and standard sirens to detect cosmic opacity

In this work, we explore the potentiality of future gravitational wave (GW) and Type Ia supernovae (SNe Ia) measurements to detect cosmic opacity by comparing the opacity-free luminosity distance (LD) of GW events with the opacity-dependent LD of SNe Ia observations. The GW data are simulated from the future measurements of the ground-based Einstein Telescope (ET) and the space-borne Deci-Herz Interferometer Gravitational wave Observatory (DECIGO). The SNe Ia data are simulated from the observations of the Wide Field Infrared Survey Telescope (WFIRST) that will be collected over the next few decades. A binning method is adopted to match the GW data with the SNe Ia data at the same redshift z with a selection criterion \begin{document}$ |\Delta z|<0.005$\end{document}, and most of the available data from the GW measurements is employed to detect cosmic opacity due to improvements in the distribution of the future SNe Ia observations. Results show that the uncertainties of the constraints on cosmic opacity can be reduced to \begin{document}$ \sigma_{\epsilon}\sim 0.0041$\end{document} and 0.0014 at the \begin{document}$ 1\sigma$\end{document} confidence level (CL) for 1000 data points from the ET and DECIGO measurements, respectively. Compared with the allowable limits of intergalactic opacity obtained from quasar continuum observations, these future astronomical observations can be used to verify the cosmic opacity. In this way, GW and SNe Ia measurements can be used as important and effective tools to detect cosmic opacity in the future.