Dynamics and gravitational radiation of binaries with spin precession and eccentricity in dynamical Chern-Simons gravity

Testing parity symmetry constitutes a critical aspect in gravitational physics. As a representative parity-violating theory, dynamical Chern-Simons (dCS) gravity has attracted significant attention in recent gravitational wave (GW) studies. Numerous works have constrained the dCS theory through GW observations using quasi-circular waveform templates. Since GW parameter estimation depends critically on waveform template accuracy, improved source modeling and waveform construction are essential for tighter constraints on parity-violating gravity. This work explores the dynamics and gravitational radiation from the binary black hole systems with orbital eccentricity and spin precession. By extending the quasi-Keplerian parameterization, we solve the equations of motion including leading-order dCS corrections and precession effects. Furthermore, the conservative sectors of the gravitational and scalar radiation are presented, the corresponding energy and angular momentum loss are calculated, and the orbital decay is also investigated. Notably, because of the non-zero monopole scalar radiation, carrying energy but not angular momentum, the zero-eccentricity orbit is no longer the final stable state of binaries under radiation reaction. This work provides the theoretical foundation for the complete waveform construction in dCS gravity, benefiting the future gravitational parity-symmetry tests.