Cosmologically we turn to the conservation of energy-mass-momentum wherein the matter fields at one point in spacetime can donate energy-mass-momentum into the

Cosmologically we turn to the conservation of energy-mass-momentum wherein the matter fields at one point in spacetime can donate energy-mass-momentum into the gravitational field, and can pick some of that up again at a distance from the gravitational field, typically changing local matter field content's (linear) momentum. At cosmological scales the "objects" are the various matter fields (in the most general sense, everything that is neither the cosmological constant nor the gravitational field itself) and we concern ourselves with energy-density, which drops with the metric expansion of space. Sean Carroll goes into some detail here: http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ http://www.preposterousuniverse.com/blog/2010/02/22/energy-i... Back to GWs: these change the peculiar motions of matter field content, at cosmological scales giving tiny nudges to galaxy clusters compared to what is imparted by Dark Energy. So even though we lose the conservation of energy, we get back the conservation of energy-momentum.