This isn't strictly an original idea. The notion that everything will collapse under the gravity of the universe into a singularity once more, is usually called "The Big Crunch".
Then of course there would be another big bang, crunch, bang, crunch, ect... for eternity.
Which would actually be a rather happy thought.
But instead, we know the universe is expanding at increasing rates. Some parts are supposedly moving away from each other faster than the speed of light. But, note that this does not in any way contradict special relativity, because it is not the objects moving through space faster than the speed of light, but rather space itself moving.
The Big Bang, isn't just the coming into existence and expansion of matter, but space and time (spacetime) as well. So space itself is expanding, and this causes parts of the universe to drift apart faster than light.. which of course by its very nature could never be observed. There would be an event horizon, so to speak, dividing us from those parts of the universe. Theoretically, of course.
Also, if such a theory is true then eventually everything will just drift so far away and die. But in a way, this causes the density of the universe to tend toward zero and so it can be thought of as returning to the nothingness that it came from.