Testing Chern-Simons Modified Gravity with Gravitational-Wave Detections
  of Extreme-Mass-Ratio Binaries
  [abridged] The detection of gravitational waves from extreme-mass-ratio
(EMRI) binaries, comprising a stellar-mass compact object orbiting around a
massive black hole, is one of the main targets for low-frequency
gravitational-wave detectors in space, like the Laser Interferometer Space
Antenna (LISA or eLISA/NGO). The long-duration gravitational-waveforms emitted
by such systems encode the structure of the strong field region of the massive
black hole, in which the inspiral occurs. The detection and analysis of EMRIs
will therefore allow us to study the geometry of massive black holes and
determine whether their nature is as predicted by General Relativity and even
to test whether General Relativity is the correct theory to describe the
dynamics of these systems. To achieve this, EMRI modeling in alternative
theories of gravity is required to describe the generation of gravitational
waves. In this paper, we explore to what extent EMRI observations with LISA or
eLISA/NGO might be able to distinguish between General Relativity and a
particular modification of it, known as Dynamical Chern-Simons Modified
Gravity. Our analysis is based on a parameter estimation study that uses
approximate gravitational waveforms obtained via a radiative-adiabatic method
and is restricted to a five-dimensional subspace of the EMRI configuration
space. This includes a Chern-Simons parameter that controls the strength of
gravitational deviations from General Relativity. We find that, if Dynamical
Chern-Simons Modified Gravity is the correct theory, an observatory like LISA
or even eLISA/NGO should be able to measure the Chern-Simons parameter with
fractional errors below 5%. If General Relativity is the true theory, these
observatories should put bounds on this parameter at the level xi^(1/4) < 10^4
km, which is four orders of magnitude better than current Solar System bounds.
