Combining chirp mass, luminosity distance and sky localisation from gravitational wave events to detect the cosmic dipole

A key test of the isotropy of the Universe on large scales consists in comparing the dipole in the Cosmic Microwave Background (CMB) temperature with the dipole in the distribution of sources at low redshift. Current analyses find a dipole in the number counts of quasars and radio sources that is 2-5 times larger than expected from the CMB, leading to a tension reaching 5$\sigma$. In this paper, we derive a consistent framework to measure the dipole independently from gravitational wave (GW) detections. We exploit the fact that the observer velocity does not only change the distribution of events in the sky, but also the luminosity distance and redshifted chirp mass, that can be extracted from the GW waveform. We show that the estimator with higher signal-to-noise ratio is the dipole in the chirp mass measured from a population of binary neutron stars. Combining all estimators (accounting for their covariance) improves the detectability of the dipole by 30-50 percent compared to number counting of binary black holes alone. We find that a few $10^6$ events are necessary to detect a dipole consistent with the CMB one, whereas if the dipole is as large as predicted by radio sources, it will already be detectable with $10^5$ events, which would correspond to a single year of observation with next generation GW detectors. GW sources provide therefore a robust and independent way of testing the isotropy of the Universe.