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This question is motivated by Big Bang Physics/Cosmology. If eternal inflation is a good description of the universe and we live in a bubble universe then presumably our bubble nucleated at a spacetime point. Does this mean it is (approximately) a finite hypersphere and therefore has a centre?

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Do you mean a ball? Spheres don't have centres. – MBN Sep 11 '13 at 15:15
@mbn: oops yes, it couldn't be a closed manifold as it has to be continuous with the space it nucleated from. Would that be a hyperball (or less excitingly, just ball)? – John Rennie Sep 11 '13 at 16:20
BTW, This hypothesis has not been ruled out ?, followin g this article – Trimok Sep 11 '13 at 18:33
@Trimok: the cosmic bubble in that article is a region of space where the average density is anomalously low. It has nothing to do with bubble universes. – John Rennie Sep 12 '13 at 14:32

Wikipedia redirects here:

Eternal Inflation is an inflationary universe model, which is itself an outgrowth or extension of the Big Bang theory. In theories of eternal inflation, the inflationary phase of the universe's expansion lasts forever in at least some regions of the universe. Because these regions expand exponentially rapidly, most of the volume of the universe at any given time is inflating. All models of eternal inflation produce an infinite multiverse, typically a fractal.

If supposedly there is one Big Bang it follows that we exist in a three dimensional sphere on the surface of a four dimensional sphere, time being the fourth dimension.

These hypothetical bubble universes would be variations in density etc with respect to our local "universe" and there will be in three space a distribution . The inhomogeneities would not necessarily have started at a point, it could be whole regions in 3space.

There are some searches suggested

Two research papers published in Physical Review Letters and Physical Review D are the first to detail how to search for signatures of other universes. Physicists are now searching for disk-like patterns in the cosmic microwave background (CMB) radiation -- relic heat radiation left over from the Big Bang -- which could provide tell-tale evidence of collisions between other universes and our own.

It is a model going away from a homogeneous universe into multiple isolated regions within the large universe from the Big Bang.

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I and Google struggled to find a definitive answer, though I did find However it still isn't clear to me what the answer is. – John Rennie Sep 11 '13 at 11:21

I tried to comment on my original question about centers as well but got locked out. First off, it is a good question and should not lead to Markov chaining, secondly, a classical description by macroscopic beings with testable observables needs only a 4D space-time descriptive value. A "cosmic egg" or balloon's surface analogy representing inflation is inaccurate. 3D space with Time taking on the 4th Dimensional value is like a 3D cube with a smaller cube glued to each of the 6 sides of the bigger cube. Picture the little cubes intersecting the bigger cube internally and perpendicularly along any imagined rotation of axis and you get 4D Space-Time. Two very differently accelerated observers can literally cross paths within nanometers in this space and due to different accelerations both observers experience time differently within the confines of the same space. What I was alluding to is, does it not seem plausible to think of the big bang as have having happened everywhere instead of originating from a mathematical point? A singularity by definition means too many unknowns and a biblically biased model lacks true explanatory power. Dr. Lawrence Krause advocates an eternal Universe and I see wisdom here. These models were all created long before anyone was aware of Dark energy or Dark matter. Dr. Allen Guth's original inflation hypothesis included "reverse" gravity. Its time for the Neanderthals to rise up against their Mutant Masters and find real answers to the cosmic chicken or egg. BTW I'm a relativist of the first order jj.

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Daniel, I imaging the mods will delete this as it's not an answer. You should be able to update your original question. If you can't ask a mod for help. I have to confess I found your original question unclear, which is part of the reason I posted this one. – John Rennie Sep 11 '13 at 13:20
I was simply baffled by the logical inconsistency of centeredness vs non-centeredness. Its been a conundrum I cant quite reconcile and would really love to be dazzled with an explanation that doesn't parrot some established view of the status quo. I'm new to this valuable resource and don't want to cause too many ripples in this pond of discussion but I do respect everyone's input. – Daniel Park Sep 11 '13 at 14:14
Daniel, it's possible that the bubble universe starts then evolves in the same way as an FLRW universe, so for it's occupants it is spatially infinite even though as measured in the external observers it is finite. In that case the bubble universe would have no centre. – John Rennie Sep 11 '13 at 14:16

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