The math is correct. Linearized GR and Newtonian gravity are qualitatively and quantitatively different and at "relativistic" scales we should probably see a di

The math is correct. Linearized GR and Newtonian gravity are qualitatively and quantitatively different and at "relativistic" scales we should probably see a difference! I don't have the cosmology background to evaluate more than that unfortunately; it's just that the "Standard Model" of cosmology uses a toy solution of GR (FLRW + newton). That said, it'd be wild if any major case of dark matter is just an artifact of incorrect approximations.