On the measurement of the speed of gravitational waves

The accurate measurement of the speed of gravitational waves (GWs) is very important for fundamental physics. In this paper, by taking cosmological effect into consideration, we derive a new formula to calculate the speed of GWs on the basis of GW 170817-like events. We find that in the case of high redshift, the luminosity distance used in the previous calculation of the speed of GWs needs to be replaced by co-moving distance. We consider some possible electromagnetic counterparts of gravitational-wave events which can significantly reduce the intrinsic uncertainty between the emission times of the gravitational and electromagnetic signals. Optimistically, the measurement accuracy will be improved to ∼10-18\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 10^{-18}$$\end{document} m  s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}.