Professors Paul J. Steinhardt and Neil Turok (the later now the head of the Perimieter Instititute here in Waterloo, Ontario and a former student of Hawking) have postulated this theory as well. In their book, Endless Universe: Beyond the Big Bang, they provide a simple and extremely elegant theory that explains how this happens, and more importantly, that their endless, cycling universe theory is the best way to explain away all of the fudges and math fixes needed to explain traditional Big Bang theory.
If we need to have hacks and fudges in the standard inflationary Big Bang theory, and we do, then it's probably wrong. Turok and Steinhardt's theory will, within a decade, have the necessary experimental evidence to be shown right or wrong so we'll soon know. The elegance of their theory, despite its reliance on some string theory that has yet to be experimentally demonstrated, is that it explains all of our observational evidence, without additions or fudges, as well as tying in our fundemental knowledge of things like conservation of energy, etc.
I, for one, welcome our balloon-like universe overlords.