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Gravitational waves (GWs) from compact binary stars at cosmological distancesare promising and powerful cosmological probes, referred to as the GW standardsirens. With future GW detectors, we will be able to precisely measure sourceluminosity distances out to a redshift $z\sim5$. To extract cosmologicalinformation, previously proposed cosmological studies using the GW standardsirens rely on source redshift information obtained through an extensiveelectromagnetic follow-up campaign. However, the redshift identification istypically time consuming and rather challenging. Here, we propose a novelmethod for cosmology with the GW standard sirens free from the redshiftmeasurements. Utilizing the anisotropies of the number density and luminositydistances of compact binaries originated from the large-scale structure, weshow 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 EinsteinTelescope would be comparable to or even better than the other large-scalestructure probes at the same epoch, and (iii) the cross-correlation with othercosmological observations is found to have high-statistical significance,providing additional cosmological information at very high redshifts.

Anisotropies of gravitational-wave standard sirens as a new cosmological probe without redshift information