My question related kind of to asking what the shape of the universe is. Say a hypothetical alien civilization built an faster-than-light spaceship. If they keep flying would they end up where they began? ie space itself is curved...or would they hit some invisible barrier?
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2"Say a hypothetical alien civilization built an FTL spaceship [..] would they hit some invisible barrier" -- I'd say aliens capable of bypassing the laws of physics are unlikely to experience any 'barrier'. – Johannes Jul 27 '14 at 06:28
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possible duplicate of Is the universe flat? – Brandon Enright Jul 27 '14 at 06:28
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How does an FTL drive like Alcubierre violate any laws of physics. It could be possible in theory atleast. – user56147 Jul 27 '14 at 08:44
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possible duplicate of Shape of the universe? – John Rennie Jul 27 '14 at 09:35
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@user56147 - an Alcubierre drive is a fantasy device that is remotely compatible with the laws of physics. However, this hypothetical device shrinks distances rather than yielding faster than light travel. – Johannes Jul 27 '14 at 11:56
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Related question on Astro.SE: http://astronomy.stackexchange.com/q/5960/476 – Qmechanic Jul 30 '14 at 14:31
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We can't peek deeper than a certain distance away from our current cosmic position, but we know for sure that the universe extends far beyond that cosmic horizon. In fact, for all we know, although our observable universe is finite, the full universe is infinite in size.
If this is indeed true (and there is no single piece of evidence against an infinite universe), the universe started infinite in size, and it has been expanding ever since. It is true that going back in time based on our deepest laws of physics we hit a singularity, but this is a temporal singularity, not a spatial singularity.

Johannes
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Interesting. While space certainly could be infinite, would that mean the number of stars and galaxies are infinite. If the number of stars is finite, someone standing on a planet at edge of the universe (and I use this term to only imply the astronomical bodies), would only see light on one side? – user56147 Jul 27 '14 at 19:27