  The inspiral of binary systems in vacuum is controlled by the stress-energy
of gravitational radiation and any other propagating degrees of freedom. For
gravitational waves, the dominant contribution is characterized by an effective
stress-energy tensor at future null infinity. We employ perturbation theory and
the short-wavelength approximation to compute this stress-energy tensor in a
wide class of alternative theories. We find that this tensor is generally a
modification of that first computed by Isaacson, where the corrections can
dominate over the general relativistic term. In a wide class of theories,
however, these corrections identically vanish at asymptotically flat, future,
null infinity, reducing the stress-energy tensor to Isaacson's. We exemplify
this phenomenon by first considering dynamical Chern-Simons modified gravity,
which corrects the action via a scalar field and the contraction of the Riemann
tensor and its dual. We then consider a wide class of theories with dynamical
scalar fields coupled to higher-order curvature invariants, and show that the
gravitational wave stress-energy tensor still reduces to Isaacson's. The
calculations presented in this paper are crucial to perform systematic tests of
such modified gravity theories through the orbital decay of binary pulsars or
through gravitational wave observations.
