Bob's getting philosophical on us again!
Good question though. Space is a funny old thing. Is there space outside the universe?
The 4 forces we know and love (gravity, electromagnetic, strong and weak) weren't always 4 separate forces. At the point of the Big Bang, they were all one. However, as the universe cooled and expanded (spacetime foam, primordeal soup, lovely expressions like that come up!), they separated out into 4 separate forces (or 4 properties of one force) This is why physicists love to talk about "Grand Unified Theories", or GUTs.
Now, everything that you experience is governed by these forces. Perhaps there is stuff that is governed by forces we are unaware of, but that's getting way too into philosophy for me. However, without those 4 basic forces we would have some problems
Weak force: quarks couldn't turn into other quarks, therefore nuclear fusion couldn't happen, and stars wouldn't work
Gravitational force: to be honest, if you are way out into deep space, you wouldn't miss it.
electromagnetic force: well, the atoms in your body wouldn't stay stuck together, you would evaporate into a puff of hydrogen, oxygen, calcium and iron
Strong force: this is the fun one. That puff of atoms you've become, well, the nucleii would all explode now! Yay!
As far as we know, and theory means we are confident about this, these 4 forces (and indeed, the original unified force) only exists within the universe.
However, you know how physicists also love banging particles together in particle accelerators? One reason for doing this is to produce highly energetic collisions, reminiscent of the conditions at the very early stages of the universe. They observe these, stroke their beards and come up with reasons why things happen the way they do, and what happened when the universe was still hot and energetic.
Today the universe is far less energetic so you could reproduce our 4 forces with much less energy.
So, provided that a) the universe is expanding at a speed less than light, and b) you can travel faster than the universe is expanding, it is possible, JUST POSSIBLE that you could reach and pass the edge of the universe, and survive within a particle accelerator of some design in order to keep you in the realm of the 4 forces.
However, so that the particle accelerator could remain intact without evaporating into pure energy, it would have to be entirely inside itself. So you could have the particle collisions going off all around you, and thus make some kind of bubble of space-time around your whole contraption.
To be honest, I couldn't recommend such a journey. But it is possible. Perhaps. Maybe.
