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Assuming hypothetically that it happens now while we are alive and analyzing our observable universe. If the unobservable universe collapses in a "Big Crunch", will we see its effects in our observable portion? Or will we continue to see an expanding universe?

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Our current model of the universe assumes that it's isotropic on large scales. That means any Big Crunch would happen everywhere at the same time, just as the Big Bang happened everywhere at the same time.

Analysis of the microwave background measurements show the universe is flat to within experimental error. It's possible that the universe is closed, but on a scale much large than the observable universe. In that case any Big Crunch will come long after you and I have died, and in fact long after all the stars in the Milky Way have burned out, so we won't be around to observe it!

Mathematically it's possible for the curvature of the universe to change dramatically just outside the visible boundaries, so some parts could be contracting while others are expanding, but physically this seems very unlikely. If there were any very large scale inhomogeneities in the universe it would mean our current understanding of the universe is drastically wrong.

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If the measurements suggesting the presence of Dark Energy hold up there is no chance of a Big Crunch and we are simply living in the rather brief period when the universe looks locally flat. –  dmckee Apr 25 '12 at 19:09
    
Would dark energy in our observable universe prevent the unobservable universe from going into a Big Crunch? Even if the unobservable universe is spatially closed? –  Ocsis2 Apr 26 '12 at 1:03
    
This answer is incorrect in modern cosmology, where we know the acceleration of the universe (did't downvote, but please fix it!) The universe will not have a big crunch with 100% certainty unless the cosmological constant is dynamical and goes to zero at later times. –  Ron Maimon May 1 '12 at 21:55
    
Isn't that what he said? That the cosmological constant could change if the curvature changes outside our observable universe (and that curvature eventually affects our observable universe). –  Ocsis2 May 7 '12 at 14:19

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