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I’ve been investigating the topological Casimir effect from compactified dimensions as a mechanism to explain dark energy, and this raised a question I was hoping someone could shed some light on. I have always thought of the Big Bang as a SIMULTANEOUS decompactification of three compact dimensions, using the terminology of string theory. Is there any evidence that decompactification progressed stepwise instead? Say from a 0+1 to a 1+1 (spatial + time-like) or from a 0+1 to a 2+1 expanded dimensional space before finally acheiving a 3+1 expanded dimensional space? If so did this lead to prior false-vacuum states that might be linked to Inflation?

More specifically, is there any hint of a stepwise decompactification observable in the Cosmic microwave background, or is there any evidence of asymmetry in the Hubble expansion field? If not, why does the big-bang require simultaneous decompactification of three spatial dimensions? What is special about 3 non-compact spatial dimensions?

Related question: If there was a stepwise Big Bang dimensional decompactification, could this have lead to large scale fluctuations in the background distribution of mass/energy, leading to early structure formation?

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  • $\begingroup$ What is special about 3 non-compact spatial dimensions? It’s what we observe. I think that makes it special. $\endgroup$
    – G. Smith
    Feb 6 '20 at 5:24
  • $\begingroup$ I would be astonished if there were any evidence for stepwise decompactification. It would be a Nobel Prize-level discovery and indirect evidence for string theory, wouldn’t it? $\endgroup$
    – G. Smith
    Feb 6 '20 at 5:25
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    $\begingroup$ @G.Smith I would be astonished if there were any evidence for “compact dimensions” or for the string theory in general ;) $\endgroup$
    – safesphere
    Feb 10 '20 at 3:56
  • $\begingroup$ It seems to me that Hubble expansion itself shows the 3-familiar spatial dimensions were once much smaller than they are today (Very much smaller). Don't you find this to be convincing evidence supporting the possibility of compact dimensions? I'm not arguing that Superstring Theory is the ultimate lens through which to view the universe, but nevertheless accepting Hubble expansion and the Big Bang carries with it the implication that at least some compact dimensions were once present in our universe. $\endgroup$ Feb 17 '20 at 17:24
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I do not know of any talk of stepwise decompactifications as you describe, but in the setting of string theory you might be interested in reading about the proposal of "String Gas Cosmology". In particular, section 5 of the article Superstrings in the early universe is an attempt at explaining a scenario where spacetime starts with 9+1 dimensions compact, and why 3+1 dimensions then decompactify.

The heuristic explanation is that winding modes oppose decompactification as it costs energy. So in order to continue decompactification there has to be a thermal equilibrium where winding strings turn into non-winding string modes. This can only happen when two winding string worldsheets intersect. In non-compact spacetime dimensions greater than 4, string world sheets are generally unlikely to intersect, and they would therefore go out of equilibrium. Therefore any decompactification beyond 4 spacetime dimensions is stopped by the negative pressure of winding states.

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    $\begingroup$ Thanks for your insight and suggested reference on SGC. Since I made this post, I also found the following reference: An anisotropic universe due to dimension-changing vacuum decay; H. C. Scargill, J. of Cosmology and Astroparticle Physics (2017), which pretty much addresses the exact question I posed re.: CMB. See also: Evidence for anisotropy of cosmic acceleration by Colin et al. Astronomy & Astrophysics (2019). That paper indicates that there may well be anisotropy in Hubble expansion, though the authors do not attribute it to step-wise decompactification. Controversial, of course. $\endgroup$ Feb 17 '20 at 17:11

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