Dark matter: an efficient catalyst for intermediate-mass-ratio-inspiral events.

The dark matter(DM) minihalo around a massive black hole(MBH) can be redistributed into a cusp, called the DM minispike. A stellar compact object inspirals into such a MBH (from $10^3 \sim 10^5$ solar masses) harbored in a DM minispike, forms an intermediate or extreme mass-ratio inspiral (IMRI or EMRI). The gravitational waves (GWs) produced by such kind of systems will be important sources for space-based interferometers like as LISA, Taiji and Tianqin. We find that due to gravitational pull and dynamical friction of the dark matter minispike, the merger time of IMRIs and EMRIs will be dramatically reduced. Our analysis shows that this effect can greatly increase the event rates of IMRIs for space-based GW detectors comparing with the previous estimation. We point out just based on the IMRI detection events by LISA, Taiji and Tianqin, we can constrain the density profile and physical models of dark matter. Furthermore, due to the faster merger of small objects with intermediate black holes, the faster growing up of black holes will be, and then the mass distribution of the MBHs will be different from the popular opinion.