A cosmological view of extreme mass-ratio inspirals in nuclear star
  clusters
  There is increasing evidence that many galaxies host both a nuclear star
cluster (NC) and a super-massive black hole (SMBH). Their coexistence is
particularly prevalent in spheroids with stellar mass 10^8-10^10 solar masses.
We study the possibility that a stellar-mass black hole (BH) hosted by a NC
inspirals and merges with the central SMBH. Due to the high stellar density in
NCs, extreme mass-ratio inspirals (EMRIs) of BHs onto SMBHs in NCs may be
important sources of gravitational waves (GWs). We consider sensitivity curves
for three different space-based GW laser interferometric mission concepts: the
Laser Interferometer Space Antenna (LISA), the New Gravitational wave
Observatory (NGO) and the DECi-hertz Interferometer Gravitational wave
Observatory (DECIGO). We predict that, under the most optimistic assumptions,
LISA and DECIGO will detect up to thousands of EMRIs in NCs per year, while NGO
will observe up to tens of EMRIs per year. We explore how a number of factors
may affect the predicted rates. In particular, if we assume that the mass of
the SMBH scales with the square of the host spheroid mass in galaxies with NCs,
rather than a linear scaling, then the event rates are more than a factor of 10
lower for both LISA and NGO, while they are almost unaffected in the case of
DECIGO.
