This question is based on the ever popular misconception that the
Universe is some curved object embedded in a higher dimensional space,
and that the Universe is expanding into this space.  This
misconception is probably fostered by the balloon analogy that shows a
2-D spherical model of the Universe expanding in a 3-D space.

While it is possible to think of the Universe this way, it is not
necessary, and---more importantly---there is nothing whatsoever that
we have measured or can measure that will show us anything about the
larger space.  Everything that we measure is within the Universe, and
we see no edge or boundary or center of expansion.  Thus the Universe
is not expanding into anything that we can see, and this is not a
profitable thing to think about.  Just as Dali's Crucifixion is just a
2-D picture of a 3-D object that represents the surface of a 4-D cube,
remember that the balloon analogy is just a 2-D picture of a 3-D
situation that is supposed to help you think about a curved 3-D space,
but it does not mean that there is really a 4-D space that the
Universe is expanding into.

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