In the spirit of effective field theory, the standard-model extension (SME) provides a comprehensive framework to systematically probe the possibility of Lorentz/$CPT$ violation. In the pure gravity sector, operators with mass dimension larger than 4, while in general being advantageous to short-range experiments, are hard to investigate with systems of astronomical size. However, there is exception if the leading-order effects are $CPT$-violating and velocity-dependent. Here we study the lowest-order operators in the pure gravity sector that violate the $CPT$ symmetry with carefully chosen relativistic binary pulsar systems. Applying the existing analytical results to the dynamics of a binary orbit, we put constraints on various coefficients for Lorentz/$CPT$ violation with mass dimension 5. These constraints, being derived from the post-Newtonian dynamics for the first time, are complementary to those obtained from the kinematics in the propagation of gravitational waves.

• Received 17 September 2018

DOI:https://doi.org/10.1103/PhysRevD.98.084049