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The measurement of the Hubble-Lema\^{i}tre constant $(H_0)$ from the cosmicmicrowave 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 GWdetector networks, it will be possible to constrain $H_0$ better than $2\%$(which is enough to resolve the tension) with binary black hole systems, alsocalled dark sirens. Bright sirens like binary neutron star systems can alsohelp resolve the tension if both the GW and the following electromagneticcounterpart are detected. In this work, we assess the potential of usingneutron star-black hole (NSBH) mergers to measure the Hubble-Lema\^{i}treconstant, both as dark sirens as well as bright sirens, thus, assigning themthe term gray sirens. We find that the Voyager network might be able to resolvethe tension using NSBH mergers in an observation span of 5 years, whereasnext-generation networks which include the Cosmic Explorer detectors and theEinstein Telescope will be able to measure the $H_0$ to sub-percent level.

Using Gray Sirens to Resolve the Hubble-Lema\^{i}tre Tension