  We study the global decay properties of solutions to the linear wave equation
in 1+3 dimensions on time-dependent, weakly asymptotically flat spacetimes.
Assuming non-trapping of null geodesics and a local energy decay estimate, we
prove that sufficiently regular solutions to this equation have bounded
conformal energy. As an application we also show a conformal energy estimate
with vector fields applied to the solution as well as a global $L^{\infty}$
decay bound in terms of a weighted norm on initial data. For solutions to the
wave equation in these dynamical backgrounds, our results reduce the problem of
establishing the classical pointwise decay rate t^{-3/2} in the interior and
t^{-1} along outgoing null cones to simply proving that local energy decay
holds.
