They don’t know. Space can be flat, have a positive curve, or a negative curve. If its flat or negative it doesn’t have a boundary and is infinite in all directions(in current theories). If its positively curved, it still doesn’t have a boundary, but if you travel in a straight line your path will eventually come back to your starting point.
The issue is that ANY curvature, no matter how small, counts. Right now our best measurements indicate its likely flat, but there is still uncertainty to the positive/negative. You have to be able to get a perfectly accurate measurement for flat (which is supposedly impossible), or one where there error margin is only in positive or negative for the curved spaces to know for certain which way it is.
We don’t know this. But think of it another way, (edit adding in this part to be more clear) *if it is a flat universe with no curvature to bend back around*, and if the universe does end, what’s past the boundary then? By definition if something is past the boundary, then that something would also be part of the universe. Even if it’s nothing, then it’s still a vacuum that would be part of the universe. So having a boundary doesn’t make sense.
The universe is expanding, which we know because objects are uniformly moving away from Earth and much faster than we’d expect given everything else we know about them and how they are moving relative to us. It’s better to think about this less as a wave of “something” flowing into “nothing” but rather as a big web of “something” where the distances between each thing are getting bigger. The farther away something is, the greater this inflation of empty space. This is one sense in which we could never reach the “boundary” to space.
The other sense is that once something is sufficiently far away from Earth, the expansion of the universe is such that we can never reach it, even if we travelled directly towards it at the speed of light. Conversely, only part of the universe is close enough to Earth that light from it has ever reached us. We call this the “observable universe,” and for many purposes, you can think of it as the bounded region of space that you have in mind. While it’s incredibly unlikely that a human will ever reach the distant reaches of the observable universe, it’s technically possible, and light generated on Earth (or, more realistically, by our sun) is making that journey now. However, it’s currently considered impossible (absent truly weird stuff like wormholes) to leave the observable universe.
To have a boundary would mean a wall needs to exist since empty space is already empty.
So for such a ridiculously huge wall to exist is even harder to comprehend.
If the boundary of space is supposed to just have nothing, then that is just empty space since an empty space is nothing so no boundary is reached either.
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