Also regarding the "center" of the Universe: the reason that "everywhere is the center" is because the Universe exists in higher than three dimensions. Asking "where is the center of the Universe" is like asking where the center of the surface of a balloon is. The center of the balloon is not on the surface in the 2D Universe.
The center of the Universe is the Big Bang, which is physically located at the beginning of time. Gravity is a depression on the surface of the Universe, which is why gravity and time are related: it literally brings us closer to the past :)
(Also note: physics is not my expertise, so take what I say with a giant grain of salt. I have just thought about this a lot over the years)
These are the properties of our universe, and of course we'll only ever have one to study. But words change, right? Atoms are no longer indivisible. Black holes are no longer fully black. So I'm really going for the properties that a thing must have in order to be considered a universe, so we don't end up with a change that's obnoxious. I'd hate it if "universe" eventually just meant "any old really big astronomical structure".
Perhaps the laws of physics would allow for different kinds, they just aren't ours (Lee Smolin's "Life of the Cosmos" is a fun exploration of this, recommended).
Overall I like your descriptions, but I'm going to have to do some thinking about the direction of a gravitational depression being one that points towards the past. I'm under the impression that many cosmologists reject the idea that something warped must be warped into some other dimension. The warping, I've read, can be intrinsic: Imagine a colored lens which is unevenly saturated with dye.
That’s silly. The center of the surface of the balloon is obviously the little part where you tie it off. I’m glad I could solve this universe paradox for you and all physicists in just a few seconds. Maybe I’ll get a Nobel Prize.
Consider a balloon with no tie. Like a basketball or something. The point is that the surface is elastic and the sphere is expanding. Balloons make the best metaphor for that imo. If you can think of a better one I'd be glad to hear it.
Only other thing I can think of is a "rubber bubble" which... is a balloon.
I often think of it as a soap bubble, but I have to stop and check myself: are we choosing spherical because that's simple, or because we have evidence? It could be toroidal or something even more bizarre.
I see it as a sphere because of the uniform expansion of the Universe. The Universe might just be so large that any measurable difference in the rate of expansion is outside the observable Universe, which could suggest a shape other than a hypersphere, but I don't subscribe to that school of thought.
The center of the Universe is the Big Bang, which is physically located at the beginning of time. Gravity is a depression on the surface of the Universe, which is why gravity and time are related: it literally brings us closer to the past :)
(Also note: physics is not my expertise, so take what I say with a giant grain of salt. I have just thought about this a lot over the years)