Well we don’t know the natural shape of a universe. Perhaps the shape requiring the least amount of effort is saddle shaped.
But I think you’re considering “flat” as the surface of a sphere - somewhere it’s possible to start at point A and return to point A. But that’s a 2-D surface on a 3-D object. It’s more like (but not) being inside the sphere and trying to get back to your starting point by going in a straight line.
The Big Bang didn’t fling material out of a central point into the surrounding space. It created the very fabric of space (and time) itself!
This means it’s not quite as intuitive for a couple of reasons:
you might expect that our ever expanding universe is adding new “space” at the edges as it spreads into infinity. That’s not quite right. Our current understanding is that the smallest unit of measure possible in our universe is something called the Planck Length. The same way that the picture on your TV is granular at the level of a pixel, our universe is granular at the level of a Planck. And instead of growing at the edges (adding new pixels to the edge of the TV screen) our universe grows by adding new Plancks in between existing ones (push two pixels in the middle of the screen aside and put in a new one in between).
If you were to walk along the surface of the Earth, what you’d find is that you are NOT walking in a straight line. You are curving along the surface of the Earth. A curved space time isn’t like that. If our universe was curved, you could move in a truly straight line – ie if you started on Earth and walked forward, you’d eventually need to leave the surface at a tangent to the curve of the Earth. But even though you’re TRULY moving in a straight line, in a curved universe you’d end up back where you started.
Except that you could never make it. The fastest speed anything can move at within the universe is the speed of light, but two points can move away from each other at an effective speed that’s faster than light! that’s because they aren’t literally moving apart faster than light, rather the space between them is growing because new planck-sized bits of space are appearing between them.
So yeah – our universe expanding rapidly in all directions doesn’t actually have any bearing on whether or not the fabric of space time is flat or not. We can’t figure out the curvature of space just because our observable universe (The area that light can actually reach us from) is a “sphere”.
By the way, space obviously DOES curve – in the presence of matter, which curves space time in a way we see as gravity. But the question is whether the universe itself, absent any matter, is flat or not.
This is a very common misconception. The way that the Big Bang is taught, people often think of all matter being squished down into a point, and then expanding outward into a 3d space that already existed. The 3d space did not exist.
Think of it this way. Stick a flag somewhere out in space. This flag never, ever moves. It stays right where it is, always. Now stick another flag out in space, say 100 million miles away from it. This second flag also never, ever moves. Even though neither flag moves, they both end up moving away from each other. Both flags are not moving. So how can they move away from each other if neither one is moving? The space itself between them is expanding. And it’s not just these two flags. Space everywhere is expanding.
Now, rewind the universe backwards in time. Again, those two flags never move, at all. But they keep getting closer to each other, just because as you go back in time, the space itself is getting smaller. As every point in space gets closer and closer together, eventually all of the points is space itself squish down into a single point.
So it’s not that matter started out as a single point and expanded into an already existing space, but instead, matter and space itself were all squished down to a single point. That point two feet away from you? That was squished down into that single point. That flag that’s 100 million miles away, that point also gets squished down to the single point. And, importantly, the flag never moved. Space itself squished.
Admittedly, this is kinda hard to grasp, since we are constantly thinking of everything in terms of an already existing 3d space.
Here is another analogy that might help. Imagine that instead of being a 3d person, you only have two dimensions. As far as you are concerned, the universe is a flat sheet of paper. You can go in the X direction, and you can go in the Y direction, but you can’t go up off of the paper. There is no Z direction in this imaginary 2d universe. Now, imagine that instead of being a piece of paper, the universe is actually the surface of a balloon. The tricky part here is not to think of the balloon as a 3d object in 3d space, like we are used to thinking, but instead think of only the surface of the balloon. You can go in any direction along the surface of the balloon, but you can’t go up off of the surface, and you can’t go down into the inside of the balloon. You can only go around along the surface of the balloon. There are only 2 dimensions in your universe.
When the Big Bang happened, the “balloon” was completely deflated, so all of the bits of the balloon are packed down right next to each other. Then the balloon inflates, and they all spread out away from each other. The balloon keeps getting bigger and bigger, so if you draw a dot on the surface of the balloon and draw a dot about an inch away from it, neither dot moves, but as the balloon inflates, the dots keep getting farther away from each other.
A “flat” universe is like your piece of paper. Only it’s a stretchy piece of paper, and it keeps expanding. A “curved” universe is like the balloon. If you keep going in one direction along the surface of the balloon, you’ll eventually get back to where you started.
So the real universe is kinda like that, except in 3 dimensions instead of 2. If you pick a direction and go that way forever, do you keep going, or do you come back around to where you are now, even though you never turned? That’s the flat vs. curved universe theories.
I’m sure I’m not the only one who’s thought of this but…
You know how on very small scales there duality - like a photon can be a wave or a particle depending on how you look at it?
Could there be some kind of duality on very large scales?
What kind of duality are you thinking of? As it stands, your question is too vague to answer.
That the universe could be flat, curved, AND closed depending upon how you measure it.
I can’t see any way that could work, at least not in the sense that we’re talking about here.
So no Nobel prize for zoid? 
If the space between everything is expanding like a balloon, wouldn’t it appear that “stuff” farther away would appear to be accelerating faster? Like if you were toward the center of the balloon, and looking at the edges, the edges would accelerate quicker than the objects closer to you, but the volume increases consistently, Ie. constant speed of light.
It’s probably already been explained or debunked over my head in this thread, but these threads with expert folks are fascinating.
Yes. This is called “Hubble’s Law” and as the name implies, credit for the discovery generally goes to a guy named Edwin Hubble (though technically another guy discovered it first).
This is the same guy that the Hubble space telescope is named after.
You’re not quite getting the balloon analogy. It’s meant to be a 2-dimentional analog, so the inside and outside of the balloon are not part of the analogy. Just the surface. So there is no center of this 2D analog, just as there is no center of the universe.
Well de Sitter space allows slicings where the spatial sections can be flat or curved and can be closed too. It depends on your coordinate choice. de Sitter space can be regarded as a cosmological model, but it’s lack of matter makes it an unrealistic one.
This month, in Universe shapes:
The Universe is 41 times more likely (?) to be closed than flat.
Or
There’s a 99% chance the Universe is closed. (This article has some nice art and explanation of some of this.)
Next month: there’s a 1 in 42 chance that the Universe sits on the back of a Hyper-Turtle.
And again, this all depends on these few specific new results being correct, which they might or might not be.
I was never sure, are those games* spherical* worlds, or toroidal? Or is it possible to distinguish the two given what we know (that going past the top of the screen brings you back to the bottom, and going past the left edge brings you to the right side, and vice versa)?
Most edgeless video game worlds (including Asteroids) are toroidal, and yes, it’s possible to tell the difference.
If our Universe is toroidal, or some other non-trivial topology, however, it’s on scales too large for us to see any of the repetition. And yes, we’ve looked.
Okay, if the universe is “flat” and finite, it has an edge, right? What would the edge of space be like?
I once saw a science fiction movie where a spaceship was propelled to the edge of space. It was like a solid wall, that wasn’t an actual thing, but just the absence of space. I don’t think that’s accurate … or is it?
An Asteroids screen is flat, finite, and edgeless. And there are other similar arrangements.
Personally, I favor rhombic dodecahedrons, just because they’re cool.
I thought we’d established that an Asteroids screen is a torus? And a torus isn’t “flat,” is it?
Your basic Asteroids torus is perfectly flat, in the sense that it has zero curvature everywhere, which is clear since it locally looks like 2-d Euclidean space.