Anisotropies of gravitational-wave standard sirens as a new cosmological
  probe without redshift information
  Gravitational waves (GWs) from compact binary stars at cosmological distances
are promising and powerful cosmological probes, referred to as the GW standard
sirens. With future GW detectors, we will be able to precisely measure source
luminosity distances out to a redshift $z\sim5$. To extract cosmological
information, previously proposed cosmological studies using the GW standard
sirens rely on source redshift information obtained through an extensive
electromagnetic follow-up campaign. However, the redshift identification is
typically time consuming and rather challenging. Here, we propose a novel
method for cosmology with the GW standard sirens free from the redshift
measurements. Utilizing the anisotropies of the number density and luminosity
distances of compact binaries originated from the large-scale structure, we
show that, once GW observations will be well established in the future, (i)
these anisotropies can be measured even at very high redshifts ($z\geq 2$),
where the identification of the electromagnetic counterpart is difficult, (ii)
the expected constraints on the primordial non-Gaussianity with the Einstein
Telescope would be comparable to or even better than the other large-scale
structure probes at the same epoch, and (iii) the cross-correlation with other
cosmological observations is found to have high-statistical significance,
providing additional cosmological information at very high redshifts.
