  We show that gravitational waves have the potential to unravel the
microphysical properties of dark matter due to the dependence of the binary
black hole merger rate on cosmic structure formation, which is itself highly
dependent on the dark matter scenario. In particular, we demonstrate that
suppression of small-scale structure -- such as that caused by interacting,
warm, or fuzzy dark matter -- leads to a significant reduction in the rate of
binary black hole mergers at redshifts $z\gtrsim5$. This shows that future
gravitational-wave observations will provide a new probe of physics beyond the
$\Lambda$CDM model.
