It's funny you ask because I've been researching this for the last two weeks after my Best Rocket Research Project.
The only proper answer is "We don't know
We have never observed a barrier or a limit to the universe so we can't see beyond it.
HOWEVER. Science has not given up on explaining that question. There is no consensus but there are competing theories.
The Evidence for the Multiverse
Part of the Big Bang Theory. Alan Guth theorized the expansion of the universe billionths of second into it's begining. His math suggest that certain particles could cause gravity to work in reverse in a VERY Large Way exponentially. This force could take the space the size of a molecule and expand it to the size of Galaxy in several billionths of a blink of an eye. This theory is largely accepted.
A Russian Physcist Vilenkin inspired by this theorized what would slow down inflation. His theory suggest that inflation doesn't end every where at once so pockets of space are expanding at different speeds suggestion there were multiple Big Bangs. Always occuring. That inflation may never end spawning multiple universe WITHIN SPACE
According to the math there is an incredible amount of energy or Dark energy in empty space at the Quantum Level.
However when we compare that with the amount of energy actually in space to push galaxies apart at the observed speed comes to an incredibly small number .01 to the hundredth 23rd power. Nothing like the math suggest.
separately attempted to explain the smallest quanta of energy in matter which turns out to be packets of energy. This theory works ONLY if these strings vibrate in 6 additional directions than the 3 Dimensions. According to the math there were extra dimensions curled up in normal space that help define the normal 3 Dimensions of Space and Time. But there were so many variation of the results that it implied a nearly infinite number of dimensions all valid. 10 to power of 500 shapes of string theories.
If our universe is part of a multiverse of an infinite amount of universes then every value of dark energy would be represented some where in one of these universe and would add up to the HUGE number physics say it should be. String Theory allows for every value of Dark Energy.
In some of those universes Dark Energy would propel universes with a small DE
number than ours to collapse and ones way too big DE
number to expand out of control so that nothing like stars and planets could come together. These three ideas individually created for their own purposes support the theory of the multiverse.
Supporters & Creators of the Multiverse
After Hawking's claim 30 Years ago that information would be lost in a blackhole because of thermal Dynamic evaporation of the singularity he began supporting the Multiverse theory when it allowed a new concept through multiverse to not only disprove his theory but also the results that disproved his older theory.
Theories of Multiverses
You should know thatGeneral Relativity allows for an infinite Universe. But we don't know. If it's Infinite then the expansion is irrelevant because there is no boundary.
If it's not, here are the possibilities
Type One Multiverse
This multiverse is just an extension of our own infinite Universe it is part of our Space but distanced so far away that light from it will never reach us. Max Tegmark estimates that such a Universe, similar to ours, should be about 10^10^115 meters away from our Universe.
Type Two Multiverse
This Multiverse is made of an infinite number of giant soap bubbles that float in hyperspace (the bulk). Each bubble contains an entire universe. In the infinite vastness of the hyperspace there are an infinite number of bubbles containing a Universe like the one we are living in, and a infinite variety of other Universes. What is more interesting is that these bubbles spawn new baby universes by colliding with each other creating a hierarchy of universes, a tree of Universes.
Type Three Multiverse
Quantum mechanics predicts, and indeed experiments done on single particles provide the evidence, that each constituent of matter can find itself in several places at the same time (see Double-slit experiment
). When you zoom in to the quantum level everything becomes foggy. Yes, every particle is to be found in several dimensions (universes) at the same time, that is, in several universes that are in the same space and time as our universe but from other dimensions inaccessible to us. There is a parallel universe out there where you don’t read this article or you may have never been born.
Type Four Multiverse
The Type 4 Multiverse contains all universes resembling our own, but also includes those having physical laws different from ours. The vast majority of the universes with these tweaked laws of physics may not be able to harbor life at all and probably are dull dark places with nothing interesting to show.
READ HERE FOR A SIMPLER EXPLANATION
-If the universe is infinite then it's expanding into "nothing". No edges and so "nothing" to expand into.
-If it is part of a multiverse then one type of verse is one where all the dimensions are right beside each other much like Trek shows being out of phase. This is where the concept of the Terseract comes in (4D cube)
-The other type of Multiverse is as explained above. Where the Universe exist in an expanding Hyperspace of other universes that are also expanding but forever cut off from one another. Universe come into being when two universe's outer membrane collides.