Probing Dark Matter Spikes via Gravitational Waves of Extreme Mass Ratio Inspirals

he exact properties of dark matter remain largely unknown despite theaccumulating evidence. If dark matter is composed of weakly interacting massiveparticles, it would be accreted by the black hole in the galactic center andform a dense, cuspy spike. Dynamical friction from this spike may haveobservable effects in a binary system. We consider extreme-mass-ratio inspiral(EMRI) binaries comprising massive black holes harbored in dark matter spikesand stellar mass objects in elliptic orbits. We find that thegravitational-wave waveforms in the frequency domain can be substantiallymodified. In particular, we show that dark matter can suppress thecharacteristic strain of a gravitational wave at low frequency but enhance itat a higher domain. These effects are more dramatic as the dark matter densityincreases. The results indicate that the signal-to-noise ratio of EMRIs can bestrongly reduced near $10^{-3}\sim 0.3$~Hz but enhanced near $1.0$~Hz with ahigher sensitivity, which can be probed via the future space-bornegravitational-wave (GW) detectors, LISA and TAIJI. The findings will haveimportant impacts on the detection and parameter inference of EMRIs.