Precise peculiar velocities from gravitational waves accompanied by electromagnetic signals and cosmological applications

Peculiar velocities are an important tool to study the large-scale distribution of matter in the local universe and test cosmological models. However, present measurements of peculiar velocities are based on empirical distance indicators, which introduce large error bars. Here, we present a new method to measure the peculiar velocities, by directly estimating luminosity distances through waveform signals from inspiralling compact binaries and measuring redshifts from electromagnetic (EM) counterparts. In the future, with the distance uncertainty of GW events reducing to 0.1 per cent by future GW detectors, the uncertainty of the peculiar velocity can be reduced to 10 km/s at 100 mega parsecs. We find that dozens of GW events with EM counterparts can provide a Hubble constant H0 uncertainty of 0.5% and the growth rate of structure with a 0.6% precision in the third-generation ground-based GW detectors, which can reconcile the H0 tension and determine the origins for cosmic accelerated expansion.