I would like to clarify something that mixes cosmology and relativistic effects. Maybe I'm not understanding something or maybe there a difference of vocabulary between the cosmological and the relativistic people.
If you ask a cosmologist at which scale the relativistic effects appears (for example in N-body simulations), he will probably answer you that a problem may occur at the scale of the horizon (so at the scale of the observable Universe). If you ask the same question to a specialist of the backreaction or a specialist of general relativity I suspect that he will answer you that a problem may occur at the scale of matter inhomogeneities (so at the scale of the cosmic web, filaments and voids).
My question is : why are there these 2 point of views ?
I suspect that is because a cosmologist hypothesizes an homogeneous space-time background and apply a perturbation theory on this background whereas for a people from general relativity there is no such background. Is it the answer or I don't understand something ?