Precise peculiar velocities from gravitational waves accompanied by
  electromagnetic signals and cosmological applications
  Peculiar velocities are a precious 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 $H_0$ uncertainty of $0.5\%$ and the growth rate of structure
with a $0.6\%$ precision in the third-generation ground-base GW detectors,
which can reconcile the $H_0$ tension and determine the origins for cosmic
accelerated expansion.
