  We present the second-order gravitational dynamics for a spacetime inhabited
by matter fields which feature vacuum birefringence. The derivation follows a
perturbative variant of the covariant constructive gravity program, ensuring
diffeomorphism invariance of gravity and causal compatibility of matter theory
and gravity. A subsequent spatio-temporal split of this theory reveals the
presence of unphysical artifacts, which are cured by imposing constraints on
the gravitational constants, reducing their number from ten to seven. Within
this sector, we derive the gravitational radiation emitted by a binary system
in circular motion. The system emits massless waves which correspond to the
radiation predicted by Einstein gravity, but also massive waves, which are
generated only above a certain angular frequency threshold and are unknown to
Einstein gravity. A gravitational-wave detector modeled as sphere of freely
falling test masses shows quantitatively and qualitatively new behavior under
the influence of this radiation. The result is a prediction of gravitational
self-coupling from first principles, demonstrating the predictive power of
covariant constructive gravity for modified gravity research, especially in the
era of gravitational-wave astronomy.
