If you subscribe to Roger Penrose's theory, at the point of infinite expansion, the current "Aeon" will end and a new big bang will happen. As best I understand it, at the point of infinite expansion, there are only photons. Mass no longer exists therefore scale no longer exists. So an infinitely huge universe becomes indistinguishable from an infinitely small universe.
Basically, the way I understand it, is the probability of a Big Bang spontaneously occurring (due to the quantum fluctuations) is some godawful infinitesimally low number 0.00000...1 that for all intents and purposes is 0, but is NOT zero.
So given ungodly eons of time (googleplex ^ googleplex * graham's number, etc. of years) something with a very, very, very low probability becomes inevitable.
