  General Relativity (GR) describes gravitation well at the energy scales which
we have so far been able to achieve or detect. However, we do not know whether
GR is behind the physics governing stronger gravitational field regimes, such
as near neutron stars or massive black-holes (MBHs). Gravitational-wave (GW)
astronomy is a promising tool to test and validate GR and/or potential
alternative theories of gravity. The information that a GW waveform carries not
only will allow us to map the strong gravitational field of its source, but
also determine the theory of gravity ruling its dynamics. In this work, we
explore the extent to which we could distinguish between GR and other theories
of gravity through the detection of low-frequency GWs from extreme-mass-ratio
inspirals (EMRIs) and, in particular, we focus on dynamical Chern-Simons
modified gravity (DCSMG). To that end, we develop a framework that enables us,
for the first time, to perform a parameter estimation analysis for EMRIs in
DCSMG. Our model is described by a 15-dimensional parameter space, that
includes the Chern-Simons (CS) parameter which characterises the deviation
between the two theories, and our analysis is based on Fisher information
matrix techniques together with a (maximum-mismatch) criterion to assess the
validity of our results. In our analysis, we study a 5-dimensional parameter
space, finding that a GW detector like the Laser Interferometer Space Antenna
(LISA) or eLISA (evolved LISA) should be able to discriminate between GR and
DCSMG with fractional errors below 5%, and hence place bounds four orders of
magnitude better than current Solar System bounds.
