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The universe isn't expanding into anything. Using that word is somewhat of a misnomer. Geometry itself is changing. Fix two points, and the distance between them changes over time. The distance changes more quickly if the points start off further away (more space in between to "expand"). This has nothing to do with string theory btw. Its based in physics nearly 80 years old...
I personally don't put much stock into string theory at the moment. Maybe it will work out in the end, but I don't think its particularly promising right now.
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