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Why only three spacial dimensions
It looks as if cosmic "fine tuning" may even extend to the existence of only exactly three spacial dimensions. From a new paper at

Quote:"Although the question of why our Universe has exactly three (large) spatial dimensions is one of the most profound puzzles in cosmology – especially in view of quantum gravity scenarios such as string theory which assume nine or ten space dimensions at the fundamental level – it is actually only occasionally addressed in the literature. In this paper we propose a topological explanation for the dimensionality of space-time based on the idea that inflation is driven by a tightly knotted network of flux tubes generated in a cosmological phase transition and the fact that knots are topologically stable only in exactly three space dimensions (“knotty inflation”)."  

"We suggest a structure for the vacuum comprised of a network of tightly knotted/linked flux tubes formed in a QCD-like cosmological phase transition and show that such a network can drive cosmological inflation. As the network can be topologically stable only in three space dimensions, this scenario provides a dynamical explanation for the existence of exactly three large spatial dimensions in our Universe."

From a popularization of this at :

Quote:"We take for granted that we live in a world of three dimensions governed by the laws of physics, and don't often wonder why. But a group of physicists just hatched a new theory that they think may explain our three-dimensional universe.

Thomas Kephart from Vanderbilt University and four of his colleagues from around the world wanted to figure out why our universe seemingly has just three dimensions, especially since, as they wrote, “quantum gravity scenarios such as string theory... assume nine or ten space dimensions at the fundamental level.”

In an environment of extremely high energy, the team said that the quark-gluon plasma would have been an ideal environment for rapid flux tube formation in the very early universe.

But, crucially, they noted that this would only work if the universe existed in three dimensions. If you add more dimensions, the process becomes unstable.
“Of all possible dimensionalities of space, our mechanism picks out three as the only number of dimensions that can inflate and thus become large,” the team wrote. “This model may explain why we live in three large spatial  dimensions,  since knotted/linked tubes are topologically unstable in higher-dimensional space-times.”

This would technically agree with a computer model from 2012 where Japanese scientists found that at the moment of the Big Bang, the universe had 10 dimensions, but only three of these spatial dimensions expanded. So, the three-dimensional space we experience could have formed from 10 dimensions, just as superstring theory predicts." 
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