The entire universe is infinitely large, (we think) but the observable universe is finite, limited by the age of the universe, the speed of light, and the portion of the early universe when space was opaque. (which is what the cosmic microwave background, or CMB is) (note that terminology is confusing; when people use the word "universe" you have to determine base on context whether they're talking about the infinite entire universe, or the finite observable universe)

Imagine an RTS game on an infinitely large map with fog of war. Sure, there's something out there beyond the fog of war, but we can't see it. (don't try to go too far with this analogy though)

The universe isn't expanding into anything. It just is. This is the key to your misunderstanding I think; the universe isn't expanding through or into some other, extra-dimensional medium. The universe itself is expanding.

Infinitely large?

My understanding was that the universe originated as a point, inflated a great deal, then began expanding at a rate that has changed over time. As a result, the universe would be significantly larger than the visible universe, but would have a finite size.

(A finite size, but no boundaries. The universe is a sphere whose circumference is everywhere but whose center is nowhere. Cue Borges music.)

It’s a common misunderstanding of the Big Bang. There is not a point where the universe originated.

Rather everything was just closer together. Imagine traveling back in time - you would see galaxies move closer and closer - until everything was super dense and hot - like the center of the sun but everywhere.

Isn’t the natural extension of things being “closer together” that they were at a singularity at some point (the Big Bang)?

Nope. The universe is infinite, according to the model. We see observe galaxies speeding away from us in every direction - and it seems unlikely that the earth was the exact center of the Big Bang.

| and it seems unlikely that the earth was the exact center of the Big Bang.

Wouldn't it be more accurate to say that everything was at the exact center of the Big Bang? Assuming it started from a singularity (which can't really be known), everything was in the center.

Wouldn't that also be consistent with a finite universe as long as the distribution of galaxies is not biased towards or away from the edge, as long as the edge itself is beyond the observable part of the universe? We wouldn't have to be in the exact center, just not too close to the boundary.

>Wouldn't that also be consistent with a finite universe

It would. It is not an unanimous conclusion that "stuff" is found everywhere in the universe and that the universe is infinitely big. However, that doesn't necessarily imply a center or an edge.

The universe might be infinite and unbounded.

The universe might be finite and bounded.

The universe might be finite and unbounded.

If the universe is finite and unbounded, we can go back to the ants on a balloon analogy. As expansion continues (and indeed speeds up) the balloon will continue to inflate, for forever. It is not possible to ever make the trip around the balloon to get back to your starting destination due to the expansion of the universe. The universe and spacetime are the 'surface' of the balloon - there is nothing inside of it, the center is not the middle of the balloon, and you cannot tunnel from one side of the balloon through to another. That isn't to say the observable universe is likely to be the extent or even close to the extent of the actual universe - it is likely still just the tiniest of fractions of the actual universe.

We're probably finite and unbounded, and expanding into nothing. As the universe expands, it creates space where it did not exist.

There's other theories that are reasonable, however. Some posit that our universe is a bubble in a true vacuum, and that there could be other bubbles containing other universes. Those theories are largely driven by the theory of inflation, which is the most accepted explanation as to how the universe expanded so far and so quickly in its early stages. (That's not to imply that the bubble multiverse theory is the most accepted explanation, though - just that most theories relating to bubble multiverses stem from looking at vacuum energy)

We probably won't know for certain in our lifetimes. Intelligent lifeforms might never know for certain.

We see stuff in all directions because the stuff extends much further than what we can observe. There may well be a 'middle' of the universe but there's no way to tell how close we are to it (or if it even exists at all.)

But...if it is infinite in extent and (nearly) uniformly dense, how would the density decrease to the current value?

Normally the term I hear is “finite, but unbounded”, but I suppose it’s hard to grok that either.

I also really wonder what is the universe “inside of”? Like why is spacetime here in the first place?

I agree that our explanation must be impoverished compared to the true nature of nature. It really boggles my mind. I enjoy the public physics lectures scattered around YouTube, but it all still leaves me realizing how limited our understanding is compared to the mundane goings ons of our universe. Our current understanding is that we’ll never communicate with distant galaxies, meaning there’s likely a trillion inhabited worlds full of beings we will never know.

There isn't really an "inside of". There is no other universe that our universe is expanding into. The universe itself just "is", it is made of space-time and that metric is expanding and accelerating. Why it exists is philosophy. Maybe it was made just for us to exist in. Maybe it doesn't give a shit about us and we're simply hydrogen left to own devices long enough to futilely question its own existence.

When we talk about the universe we're rarely talking about what do not know yet, but rather what is possible to know.

Whether there is another universe "outside" of ours is not just something we don't know. It's something we cannot know but it's also something that cannot matter. The observable universe is, by definition, the total encompassment of everything that can possibly ever matter to us in even the strictest mathematical sense.

> there’s likely a trillion inhabited worlds full of beings we will never know.

And by the time our radio signal gets to them, the ones there now will all be long dead, interpreted by some future generation. By the time we get the response, humanity may be long extinct. So for all intents and purposes, we may as well be alone in the universe.