Hoping you have some answers:
1. Is inflation as in the Big Bang coincident with compactification?
2. Is the compactification of 6 dimensions most likely or could other numbers of dimensions be just as likely?
3. I read that there may have been two inflations in the Big Bang. Is this likely?
4. If 3 is so, and I read of Randell & Sundrum's claim for larger dimensions in Scientific American (i.e., our universe lives on a brane in the larger dimensions), could the first inflation be a compactification that produced the larger dimensions, and the second inflation be a compactification that produced our universe?
5. If 26-d string theory has two time-like dimensions, then is it likely that the first inflation produced the larger 4-d spacetime and the second produced a smaller 4-d spacetime, our universe.
6. If all of the above is likely, then is it likely that the second inflation is coincident with two sets of 6-d compactifications, one which in superstring theory produced fermions, and the other which produced the supersymmetric partners of the fermions?
If all the above is still likely, then I suggest that the (electric-charge) neutral supersymmetric partners possess a different type of charge that acts analogous to electric charge, and that initially in the Big Bang, anti-symmetric partners were produced and recombined just like the anti-fermions did. That implies that dark matter is composed of the supersymmetric particles left over from recombination, but with a mass comparable to fermions
I also propose that in both cases the anti-particle/particle pairs before recombination were connected by threads of the most elementary form of compactified dimensions, and that at recombination these threads precipitated into 3-d space into what are called cosmic axions. If so, then dark matter is composed of both axions and supersymmetric partners, but with axion mass being dominant.
Is there a clue in all this as to what Dark Energy could be?