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Is it possible for the curled dimensions described in superstring theories to become uncurled and open up. I have read that the big bang could have been the uncurling over 3 dimensions through collisions of branes: http://universe-review.ca/I15-39-collision.jpg. Is their any theoretical mechanism that causes this uncurling of dimensions?

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Your diagram looks like an illustration of the Ekpyrotic universe. In this model the extra dimensions are not compactified (i.e. curled up) so there is no uncurling of them. The reason we don't see the extra dimensions is because our universe is confined to a 3D brane, not because the extra dimensions are curled up.

One well known theory for what determines the way the extra dimensions are curled up is the KKLT theory - I can't find a popular science article on this so I've linked the original paper, but the original paper will be incomprehensible to most people (including me). The most stable configuration is actually to have all the dimensions uncurled, but geometries with 3 open and 6 compact dimensions can be metastable with exceedingly long lifetimes.

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    $\begingroup$ I am sorry, KKLT is not the best current theory of moduli stabilization (i.e. the way the extra dimensions are curled up). I am neutral on this theory, but this theory receives many criticism from the community and there are some similar theories. Saying that it is the "best" is a too strong statement. $\endgroup$ – mastrok Aug 2 '14 at 10:18
  • $\begingroup$ So if our universe is confined to our 3D Brane, are the other branes related to the extra dimensions of string theory? $\endgroup$ – user122083 Aug 2 '14 at 16:15
  • $\begingroup$ By "universe", do you mean all the matter and energy we interact with, or are you referring to the spatial dimensions we move in? $\endgroup$ – HDE 226868 Aug 4 '14 at 18:42

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