  In the gravitational sector, we study the CPT violation and birefringence of
gravitational waves. In presence of the CPT violation, a relative dephasing is
generated between two circular polarization states of gravitational waves. This
effect induces the birefringence of gravitational waves. We predict the
gravitational waveform corrected by it and estimate the expected constraints on
it from Advanced Laser Interferometer Gravitational-Wave Observatory, Einstein
Telescope and Laser Interferometer Space Antenna.
