Chalnoth said:
I don't think it makes sense to think of FRW as something that can realistically be an accurate description of the universe very far beyond the observable universe. It is an approximation that works extremely well within the observable universe, but it is unlikely to extend all that far beyond that.
Well, I agree the "almost FRW" model is the best we have but it is not a model only for the observable universo, it is meant to work for the whole universe, it doesn't make sense as a model for the observable part only.
Anyway it is in the observable part where it obviously finds its problems with observations.
The first one is by construction of the model, its equations and principal assumption demand that the density parameter is independent (at large distribution scale) from spatial location, the dependence must only be temporal. This collides frontally for the purpose of direct observations and validation of the above-mentioned location density independence with the inability to separate the temporal and spatial parts in all non-static spacetimes by their own mathematical nature. In other words in such non-static spacetimes there is no well defined three-dimensional spacelike hypersurface.
This leads to the well known particularity of the FRW universe that only in preferred coordinates can we define with this model a universal time, that which sees a different density at each time t. But observationally this imposes a radial dependence of density since we observe by the finiteness of c different times with radial distance.
So we find that since we can't possibly observe the spatial features of our universo at an instant of time, we have no way to validate directly the independence of density from location(homogeneity) except indirectly and statistically. We basically infer it from the observed average isotropy. If the static models of the universe were mathematically or empirically feasible which are not (see cosmological redshift), what we observe wrt homogeneity would be compatible with the perfect cosmological principle for static cosmologies.
In this sense I find it odd that many find problems with the homogeneity assumption of the model every time we find cosmic structures(see
http://en.wikipedia.org/wiki/Hercules-Corona_Borealis_Great_Wall) that are apparently too big to be compatible with large scale homogeneity. By the problem mentioned there is no scale at which we can observe homogeneity, to do it light speed should be infinite, and we know empirically and theoretically it isn't.
What those big structures if confirmed clash with is the time evolution of the universe or finiteness of time from Bing-Bang. It seems there is no time for such a huge structure at such distance to have evolved from the Big-Bang.
