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Originally Posted by Eratosthenes
You make a good point Alex
If we assume that the Universe is extremely large - well beyond the detection limits we are capable of today - then we may observe a near flat Universe even though the Universe could have any shape or curvature imaginable.
If the Universe is indeed infinite in size, wouldn't that imply that any measurement of its curvature would be flat, irrespective of its actual shape or geometry (if shape and geometry can be applied to a truly infinite object)
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Flatness is not a criteria for an infinite surface. As has already been discussed, a 3-torus is flat but finite.
A zero curvature flat Universe is supported by the angular size of the anisotropic structures in the CMB.
If the Universe has a positive curvature the anisotropic structures would appear larger.
Conversely for a negative curvature, structures would appear smaller.