Testing the gravitational weak equivalence principle in the standard model extension with binary pulsars

The standard model extension provides a framework to systematically investigate possible violation of the Lorentz symmetry. Concerning gravity, the linearized version was extensively examined. We here cast the first set of experimental bounds on the nonlinear terms in the field equation from the anisotropic cubic curvature couplings. These terms introduce body-dependent accelerations for self-gravitating objects, thus violating the gravitational weak equivalence principle (GWEP). Novel phenomena, which are absent in the linearized gravity, remain experimentally unexplored. We constrain them with precise binary-orbit measurements from pulsar timing, wherein the high density and large compactness of neutron stars are crucial for the test. It is the first study that seeks GWEP-violating signals in a fully anisotropic framework with Lorentz violation.