If the Universe is expanding what is it expanding into

an alternate Universe?

Wish we could really know :/

If the universe is infinitely big, then the answer is simply that it isn't expanding into anything; instead, what is happening is that every region of the universe, every distance between every pair of galaxies, is being "stretched", but the overall size of the universe was infinitely big to begin with and continues to remain infinitely big as time goes on, so the universe's size doesn't change, and therefore it doesn't expand into anything. If, on the other hand, the universe has a finite size, then it may be legitimate to claim that there is something "outside of the universe" that the universe is expanding into. However, because we are, by definition, stuck within the space that makes up our universe and have no way to observe anything outside of it, this ceases to be a question that can be answered scientifically. So the answer in that case is that we REALLY DON'T KNOW what, if anything, the universe is expanding into.

Not everything in the universe is "stretching" or "expanding" in the way that the spaces between faraway galaxies stretch. For example, you and I aren't expanding, the Earth isn't expanding, the sun isn't expanding, even the entire Milky Way galaxy isn't expanding. That's because on these relatively small scales, the effect of the universe's stretching is completely overwhelmed by other forces (i.e. the galaxy's gravity, the sun's gravity, the Earth's gravity, and the atomic forces which hold people's bodies together). It is only when we look across far enough distances in the universe that the effect of the universe's stretching becomes noticeable above the effects of local gravity and other forces which tend to hold things together.

I'm afraid it doesn't have to expand into anything. I know it seems that it has to, because that is the way the world works on the scales which we experience from day to day. But just as the quantum world is quite different from the day-to-day world, so is that of cosmology. THe universe is, quite literally, 'everything'. As far as we know, there is nothing for it to expand into. As far as we know, it doesn't have any boundaries, but it is finite in extent. (I know that seems odd, too, but think of the surface of a sphere. That has a very definite area, but it doesn't have any boundaries IN THE SURFACE. THe space-time we live in may be a 4D analog of that.