Now, here's something I like thinking about.
Let's say our universe is a closed universe. Let's also assume that it's infinitely large, but it doesn't have to be. It's large on a scale that we would never be able to comprehend, anyway. I realize the concepts of a closed universe and an infinitely large universe don't mesh well
Now, for now, let's only think about what we perceive as our "universe." There's more to it, but we'll get to that. Eventually, "our universe," on a time scale so large as we cannot even imagine, will devolve into nothing. This is due to a combination of inflation and the second law of thermodynamics.
At this point, within our known universe, everything is essentially nothing. At this point, a new period of inflation pops up. This is another Big Bang. The inflation drives the universe to expand at the same rates ours did. It expands so fast, that they cannot see past their "cosmological horizon," just as we cannot currently see past ours. So eventually life evolves within this universe, but they assume that everything within their cosmological horizon is the extent of the universe.
The great part is that after a period of time approximately that which our universe has existed and has reached a similar scale, this closed universe would geometrically appear flat, just as ours does.
This would be global, eternal inflation, and I kind of like this theory.