I think it is better to say that energy conservation is not defined (currently) over cosmological distance scales.
However, Wiki claims a stress-energy-momentum pseudotensor (Landau–Lifsh*tz pseudotensor
) is a valid means of incorporating gravity energy-momentum into a total conserved "current" for a compact space-time (4-vector) region. I understand that an asymptotically flat space-time region (e.g. very far from a black hole) is a special case for energy conservation, but I don't know how non-flat or how compact a region is typically
considered, and to what extent conserved current (energy conservation) calculations are approximations within the GR framework.
A very lively, and recent, blog discussion can be found here (blog.viXra.org
) with UK physicist Phil Gibbs as the proponent for cosmic scale "energy" conservation. I'm not claiming Phil is right, as I understand this site is controversial because anything goes here(?). Though the discussion is interesting and stimulating (includes some math). It makes me wonder whether there is further understanding and interpretation to be had within the classical theory of GR.