Does space go on forever?
For most of the past century it has been believe that space is positively curved, meaning that the universe is finite but boundless, meaning you can’t leave but there is a limited amount of space. More recent evidence suggests that space is either flat or has only a very slight curvature. The discovery of inflation suggests that our intuitive views on what space is might be flawed; it would seem that space is being spontaneously generated everywhere. One of the problems to answering your question is the fact that the universe had a beginning, and inflation allows relative velocities between galaxies to exceed the speed of light. This means that there is a limit to how far we can see in any direction. It is highly likely that the universe is larger than the observable universe. Whether it is infinite probably cannot be proven, although eventually a theory requiring the universe to be either infinite or finite will gain widespread acceptance, and then you’ll have your answer, by scientif
We don’t know, but recent measurement in the variation of the fine structure constant seem to suggest the observable universe is just an exceedingly small bubble (where the laws of physics allow fusing of matter to power stars) in a massively larger ‘space’ with varying laws and physical constants.
I happen to believe the universe is infinite in space and in time. Our local universe may be only a bubble in an infinite universe, Olbers’ paradox notwithstanding. The current iteration of the local Big Bang may be one of an infinitely many cycles of Bangs and Crunches. The expansion is accelerating but we don’t know what the future holds anyway. There surely will be more surprises ahead. Even in our local universe never contracts again, it might merge with nearby universes. We don’t even know exactly what dark matter, dark energy, or dark flow are. The latter may be the first evidence of an unseen neighboring universe. Yes, I’ve thought very intensely about Olbers’ paradox, but even in a universe which has always existed, I found what I believe to be a fatal flaw, and I explained the paradox, to my satisfaction, assuming only that the universe is homogeneous and static on an Extremely Large Scale, a scale in which our local universe is but a speck.