Here is my original short article explaining some of the most common questions put forth in this sub-forum with regards to the Big Bang and the origins of space-time. Note: I use four dimensions for familiarity's sake. It can be extended infinitely without breakdown of the mathematics.
This is very interesting, kudos to you for taking the time to write it. One thing I'm confused about is how/why the "fluctuation" occurred that transformed epsilon into mu. Also, I'm wondering if particles/matter could have existed before the big bang, even though time did not?
In other universes, anything could have or does or will exist. Those universes may have a temporal dimension, it may have more than one, or may have none (like our original pre-BB manifold E_4). As for how the fluctuation occurred, if one examines the wavefunction (Schrodinger's Eqn.) on a manifold like E_4, it can be shown (and has in 2 articles I read- very very very technical though) that such an instability lies in the heart of the manifold. I plan on starting work on that research next, once I type up a decent journal article on the topic I posted here. I am done my first draft, but I want my professor advisor to look it over before I submit it to the arXiv pre-print and then eventually to a journal.