Spin-precessing black hole binaries in dynamical Chern-Simons gravity

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.