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Is the sentence in the title right that our universe is infinite? And if so does it mean that stars are not evenly distributed along our universe but they all move from a populated centre to a fairly empty region of the universe? If you think that that is not the case then why we consider that there should not be more dimensions of our universe?

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If a 2D area cannot be curved and finite is the same regarding the 3D space of our universe?

Both the premise and the conclusion are incorrect. The sphere, for example, is curved, two-dimensional and finite. Similarly, one possible cosmological model for the large scale geometry of space (not spacetime) is that of a three-dimensional sphere, which is curved and finite.

There are many examples of two-dimensional spaces that are curved and finite. For example, a torus with $n$ holes is curved and finite, and $n$ is arbitrary. Varying $n$, you get infinitely many examples of curved, but finite, two-dimensional surfaces.

The best cosmological data for our Universe suggests that space (not spacetime) is approximately flat in large scales, which implies that space is infinite. Furthermore, most spacetime models assume that spacetime (not space) is infinite, meaning that most models assume time to be infinite.

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  • $\begingroup$ Corrected!..... $\endgroup$ Commented May 7 at 18:18

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