Probing Dark Matter Spikes via Gravitational Waves of Extreme Mass Ratio
  Inspirals
  The exact properties of dark matter remain largely unknown despite of the
accumulating evidence. If dark matter is composed of weakly-interacting massive
particles, it would be accreted by the black hole in galactic center and forms
a dense cuspy spike. Dynamical friction from such a spike may have observable
effects in a binary system. We consider extreme-mass-ratio inspiral (EMRI)
binaries consisting of massive black holes harbored in dark matter spikes and
stellar mass objects in elliptic orbits. We find the gravitational-wave
waveforms in frequency domain can be significantly modified. In particular, we
show dark matter can suppress the characteristic strain of gravitational wave
at low frequency but enhance it at higher domain. These effects are more
dramatic as the dark matter density increases. The results indicate that the
signal-to-noise ratio of EMRIs could be strongly reduced around $10^{-3}\sim
0.3$Hz but enhanced around 1.0Hz with a higher sensitivity, which could be
probed via future space-borne GW detectors, LISA and TAIJI. The findings would
have important impacts on the detection and parameter inference of EMRIs.
