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Scientists Propose We Live in a Slowly Rotating Universe That Completes One Rotation Every 500 Billion Years
(www.labrujulaverde.com)
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If that is true maybe that means that it actually is finite and has a center. And the rotation and light speed put an upper bound on its size.
Then again the expansion of space doesn't care about such mundane things as a cosmic speed limit so the universe rotation probably won't either. Or the extents just slow down.
I believe just the observable part is. Could be more.