If I understand this correctly:
In the main Cosmic Inflation universe, new space is created exponentially with time.
In roughly 1 out of every 30,000 pieces of "new space", a big bang occurs from a random quantum fluctuation. The big bangs slow down the inflation expansion in a local area that becomes the equivalent of a 'pocket universe'.
There was perhaps an infinite number of big bangs (and dead pocket universes) in the past, and there will be an infinite number of big bangs (and new pocket universes) in the future.