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I believe it's an open question, the curvature of the universe, and hence whether the universe is infinite.

Others have already clarified that the big bang tells us the observable universe used to be tiny. In other words, the universe was much denser. It does not tell us the absolute size of the entire universe.



"Denser Universe" means that we were (or are) in a black hole. There is no other way around a huge mass in a small space.




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