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What prevents the unobservable universe from being a continuously enlarging sphere due to the inflating bubble universes? Our observable universe being close to flat could support such a scenario?

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Nothing. Philosophically many people prefer some sort of mediocrity principle which say that what we experience is roughly similar to what is the case everywhere else. But by definition what is unobservable is beyond the (current) scope of testable hypotheses and hence beyond the realm of science. So no scientific statement can assert anything about the "unobservable universe". –  Willie Wong Apr 10 '12 at 10:56
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Don't be mislead by the term "bubble universe". It doesn't mean the universe has spherical symmetry like a bubble. It just means the post inflation universe appears as a region within the larger bit that's still inflating. Any universe produced by inflation will be virtually flat as we discussed in Why does inflation (the inflaton field) push Omega down closer to zero (flatten the universe)?.

Having said that, you ask an interesting question and I'm not sure how the large scale geometry of a post inflation patch relates to to the geometry of the parent "multiverse". I don't think the post inflation patch "pinches off" from the multiverse, so I don't think it can have the topology of a sphere. That restricts it to the topology of a flat universe, though if it's big enough even a very small deviation from $\Omega$ = 1 will be significant.

As for the "multiverse", i.e. the bit that's still inflating, it could have any topology and we wouldn't know.

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It is annoying that people feel comfortable talking about things that are in-principle unobservable, like the stuff beyond the cosmological horizon. You might as well talk about life after death and the existence of beelzebub. –  Ron Maimon Apr 15 '12 at 6:31
We can't observe the big bang either. Why do we think it's true (or at least allowed to be talked about?). It's because it can have observational consequences on what we do observe. You could infer that the cosmic background radiation is evidence of the big bang. But if the scientists who developed the BBT weren't allowed to do so because people told them a Big Bang would never be experimentally verifiable we wouldn't know how to interpret the CMB, heck we'd probably never launch the detector that detected it! –  tachyonicbrane Jun 20 '12 at 4:48
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