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Gravitational waves (GWs) can be produced if a stellar compact object, suchas a black hole (BH) or neutron star, inspirals into an intermediate-massiveblack hole (IMBH) of $(10^3 \sim 10^5)\,M_\odot$. Such a system may be producedin the center of a globular cluster (GC) or a nuclear star cluster (NSC), andis known as an intermediate- or extreme-mass-ratio inspiral (IMRI or EMRI).Motivated by the recent suggestions that dark matter minispikes could formaround IMBHs, we study the effect of dynamical friction against DM on themerger rate of IMRIs/EMRIs. We find that the merger timescale of IMBHs with BHsand NSs would be shortened by two to three orders of magnitude. As a result,the event rate of IMRIs/EMRIs are enhanced by orders of magnitude relative tothat in the case of no DM minispikes. In the most extreme case where IMBHs aresmall and the DM minispikes have a steep density profile, all the BH in GCs andNSCs might be exhausted so that the mergers with NSs would dominate the currentIMRIs/EMRIs. Our results suggest that the mass function of the IMBHs below$10^4 \,M_\odot$ would bear imprints of the distribution of DM minispikesbecause these low-mass IMBHs can grow efficiently in the presence of DMminispikes by merging with BHs and NSs. Future space-based GW detectors, likeLISA, Taiji, and Tianqin, can measure the IMRI/EMRI rate and hence constrainthe distribution of DM around IMBHs.

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