TITLE: Is there a proof that space expanding produces observers at all points that see what we see?
QUESTION [5 upvotes]: I know that galaxies are moving away from us, and so can see that it's intuitive that if space was expanding, then the astronomical observations from Earth would be the same as at all other points in the universe. 
But it's that intuition often overlooks details. So, what I would like to know, is whether there is proof that smoothly expanding space in 4 dimensions, accommodates every observer point in this way. 
Does anyone know?

REPLY [2 votes]: You are approaching the question from the wrong end.
The expansion of the universe is described by a particular solution to Einstein's equation called the FLRW metric. To derive this metric we have to make some assumptions, and the key assumptions are that the universe is isotropic and homogeneous i.e. that it is the same everywhere.
So the universe being the same everywhere is an initial assumption that goes into describing how the universe expands. It isn't something that is derived from the way the universe expands. You can of course show that the FLRW metric implies isotropy and homogeneity (as Timaeus does) but that's because those assumptions were built into it from the beginning.
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