  [abridged] Chern-Simons (CS) modified gravity is a 4D effective theory that
descends both from string theory and loop quantum gravity, and that corrects
the Einstein-Hilbert action by adding the product of a scalar field and the
parity-violating, Pontryagin density. In this theory, the gravitational field
of spinning black holes is described by a modified Kerr geometry whose
multipole moments deviate from the Kerr ones only at the fourth multipole, l =
4. We investigate possible signatures of this theory in the gravitational wave
emission produced in the inspiral of stellar compact objects into massive black
holes, both for intermediate- and extreme-mass ratios. We use the
semi-relativistic approximation, where the trajectories are geodesics of the
massive black hole geometry and the gravitational waveforms are obtained from a
multipolar decomposition of the radiative field. The main CS corrections to the
waveforms arise from modifications to the geodesic trajectories, due to changes
to the massive black hole geometry, and manifest themselves as an accumulating
dephasing relative to the general relativistic case. We also explore the
propagation and the stress-energy tensor of gravitational waves in this theory.
We find that, although this tensor has the same form as in General Relativity,
the energy and angular momentum balance laws are indeed modified through the
stress-energy tensor of the CS scalar field. These balance laws could be used
to describe the inspiral through adiabatic changes in the orbital parameters,
which in turn would enhance the dephasing effect. Gravitational-wave
observations of intermediate- or extreme-mass ratio inspirals with advanced
ground detectors or with LISA could use such dephasing to test the dynamical
theory to unprecedented levels.
