  Gravitational waves from spin-precessing binaries exhibit amplitude
oscillations that provide an invaluable method to extract the spins of the
inspiraling compact objects. The spin-spin and spin-orbit interactions that
cause this effect are sensitive to the fundamental nature of gravity, which
will allow us to constrain modified theories of gravity using gravitational
wave observations of precessing binaries. We here consider precessing black
hole binaries in dynamical Chern-Simons gravity, an effective theory of gravity
that enhances parity violating interactions. We model the black holes as
modified point particles using effective field theory, and derive the
spin-precession equations for a binary system by working within the
post-Newtonian formalism. We find that the spin-spin and quadrupole-monopole
interactions of General Relativity are modified due to an interaction between
the scalar dipoles of the two black holes and the modified black hole
quadrupole as a result of the violation of the no hair theorems. These
modifications enter the precession equations at leading post-Newtonian order.
We further show that these precession equations admit seven constants of motion
when neglecting radiation reaction, with only the mass-weighted effective spin
being modified from General Relativity. We discuss how these may be used to
reduce the precession equations to quadrature and the possibility of
constructing analytic Fourier domain waveforms for generic spin-precessing
binaries in dCS gravity.
