Extreme dark matter tests with extreme mass ratio inspirals

Future space-based laser interferometry experiments such as LISA are expected to detect $\mathcal{O}(100--1000)$ stellar-mass compact objects falling into massive black holes in the centers of galaxies, the so-called extreme-mass-ratio inspirals (EMRIs). If dark matter forms a ``spike'' due to the growth of the massive black hole, it will induce a gravitational drag on the inspiralling object, changing the EMRI orbit and gravitational-wave signal. We show that detection of even a single dark matter spike from an EMRI will severely constrain several popular dark matter candidates, such as ultralight bosons, keV fermions, MeV--TeV self-annihilating dark matter, and sub-solar mass primordial black holes, as these candidates would flatten the spikes through various mechanisms. Future space gravitational wave experiments could thus have a significant impact on the particle identification of dark matter.