Science with the space-based interferometer LISA. V: Extreme mass-ratio
  inspirals
  The space-based Laser Interferometer Space Antenna (LISA) will be able to
observe the gravitational-wave signals from systems comprised of a massive
black hole and a stellar-mass compact object. These systems are known as
extreme-mass-ratio inspirals (EMRIs) and are expected to complete $\sim
10^4$-$10^5$ cycles in band, thus allowing exquisite measurements of their
parameters. In this work, we attempt to quantify the astrophysical
uncertainties affecting the predictions for the number of EMRIs detectable by
LISA, and find that competing astrophysical assumptions produce a variance of
about three orders of magnitude in the expected intrinsic EMRI rate. However,
we find that irrespective of the astrophysical model, at least a few EMRIs per
year should be detectable by the LISA mission, with up to a few thousands per
year under the most optimistic astrophysical assumptions. We also investigate
the precision with which LISA will be able to extract the parameters of these
sources. We find that typical fractional statistical errors with which the
intrinsic parameters (redshifted masses, massive black hole spin and orbital
eccentricity) can be recovered are $\sim 10^{-6}$-$10^{-4}$. Luminosity
distance (which is required to infer true masses) is inferred to about $10\%$
precision and sky position is localized to a few square degrees, while tests of
the multipolar structure of the Kerr metric can be performed to percent-level
precision or better.
