Using grey sirens to resolve the Hubble-Lemaitre tension

The measurement of the Hubble-Lemaitre constant (H-0) from the cosmic microwave background and the Type IA supernovae are at odds with each other. One way to resolve this tension is to use an independent way to measure H-0. This can be accomplished by using gravitational-wave (GW) observations. Previous works have shown that with the onset of the next generation of GW detector networks, it will be possible to constrain H-0 to better than 2 per cent precision (which is enough to resolve the tension) with binary black hole systems that are extremely well localized in the sky, also called golden dark sirens. Bright sirens like binary neutron star systems can also help resolve the tension if both the GW and the following electromagnetic counterpart are detected. In this work, we show that neutron star-black hole (NSBH) mergers can act both as golden dark sirens as well as bright sirens, thus, assigning them the term grey sirens. We assess the potential of using NSBH mergers to measure H-0 and find that the Voyager network might be able to resolve the tension in an observation span of 5 yr. The next generation networks, which include the Cosmic Explorer detectors and the Einstein Telescope will be able to measure H-0 to sub-per cent level just by using NSBH mergers.