If Manifold of spacetime in GR relates to a Homogenous Universe, what if the UNiverse is not Homogeous ?

Answer 1

The difference between our Universe and the Homogeneous Universe of General Relativity is very minute. By that I mean that with almost a century of testing, there have not been any results that contradict GR. While it is conceivable that the Universe is not homogeneous, the portion of the Universe we have been able to observe is very close to homogeneous.