I figured I might as well expand my earlier comment into an answer, as I've cobbled together some more information.
You're talking about the cyclic model, which states that the universe goes through cycles of Big Bangs and Big Crunches. We live in the middle of one of those cycles. Albert Einstein was one of the first to investigate it, but his efforts came to nothing.
The theory has been reincarnated, most recently in 2002 by Paul Steinhardt and Neil Turok. They propose that the cosmological constant has changed over time, which could make the accelerating expansion of the universe fit into the theory. Another good article on their idea can be found here. Roger Penrose has also come up with a theory - Conformal Cyclic Cosmology - along similar lines as Einstein's. You can use this as a starting point for more reading.
A related topic is the Big Bounce, which attempts to address the Big Bangs and Big Crunches.
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