I'm afraid you cannot see into the space the universe is expanding into, that's impossible because there is nothing there, no space, no time, nothing.
As matter (universe) expands, it creates the space and time in the void it moves into ...... classical theories had the big bang causing this expansion, which seems pretty reasonable to me when you look at all the evidence.
The problem being, did we expand forever or were we gonna slow down and gravity pull us back in again just as a ball slows down and comes back to earth when it's thrown up in the air ...it accelerates for a time and then decelerates as the effect of gravity pulls it back.
When cosmologists looked at the expanding universe, I think the expectation was one of a decelerating fringe but I'm afraid this wasn't the case....the problem here is, if we are accelerating, then it means we are doomed to become a lifeless cold, extremely cold universe.
I quite liked the idea of us coming back together in a big crunch and maybe reborn again ...... I like it because it has symmetry.
And the notion that all the world's matter and energy can be compressed into a sphere the size of an atom (just before it enters the singularity phase that mathematicians and astrophysicists love soooo dearly) does my ole nut in big time......think about it, ALL the world's matter compressed down to that size ...it's mind numbing.
It's so mind numbing in fact that at this stage of the game where mathematicians and astrophysicists are struggling for breath, a door opens up and in steps a bunch of philosophers to take over the debate ......blimey, ya know all is lost when they get into it...those guys can disappear up their own ass and still declare they have found the truth of the matter (pun intended).
Whatever the case, the jury's still out in terms of what happens after the big crunch but at least we won't be around to worry about it anyway