Quote by ThomasT
Thus, it can't be said that our universe didn't begin as some explosive event of finite extent in, say, a preexisting medium of infinite extent. There's just no way to know. But, afaik, the largest scale observations of our universe (revealing a lacelike structure of connected filaments of radiating matter with large dark voids) don't contradict such a conjecture.

Quote by Cosmo Novice
I do not think this is correct. Even if you are modelling an LQG bounce, there was no preexisting background.

How can you, or anyone, possibly know that?
Quote by Cosmo Novice
There may have been a classically contracting spacetime that led to a bounce, but I do not think this is the preexisting background you have in mind ...

I don't have any particular preexisting background in mind. Just a preexisting medium of unknown structure, and that this is a possibility that can't be ruled out. Anyway, I don't have in mind any sort of classically contracting spacetime.
Quote by Cosmo Novice
... or is even relevant to our current spacetime metric after t>planck.

It's obviously not relevant to t > Planck. We're talking about t < Planck and the possibility of a finite disturbance as the beginning of our universe  which is inherently speculative, and therefore a possibiltiy.
Quote by ThomasT
If our universe is finite (eg., a volume bounded by an expanding wave shell), then there's a region within it that we'd refer to as its center. Only if it's infinite would it have no center. Again, as marcus has pointed out, there's no way to know which it is.

Quote by Cosmo Novice
Again I think this is incorrect. Both finite and infinite models of the U rely on the key cosmological prinicple of homogeneity. This principle is invalidated if you deposit any values of differentiation, so no centers, no middles, no edges ...

Homogeneity doesn't preclude a center or edges if the homogeneous volume/medium is finite/bounded.
Quote by Cosmo Novice
...  no variation on large scales other than local variation.

I don't know what you're referring to by this.
Quote by Cosmo Novice
Finite models do not assume expansion into a preexisting background just by nature of their being finite.

Nor do they necessarily exclude it, even if they might obviate it.
Quote by Cosmo Novice
Finite or infinite the U has no spacial center or spacial edge ...

This is nonsensical. If it's finite, then, by definition, it has a spatial edge or boundary and a center. We just have no way, at least currently, of reasonably inferring that it's either finite or infinite.
Quote by Cosmo Novice
... which makes it a higher dimensional topology ...

Higher dimensional topologies are, afaik, employed for calculational purposes only, and should not be taken as literal descriptions of our universe.
Quote by Cosmo Novice
...  it did not require a preexisting space.

Ok, but this doesn't rule out the possibility of a preexisting medium/space, ie., the possibility that our universe is part of something quite larger, perhaps infinite.