In my limited understanding, Penrose suggests that the universe goes through these cycles of what can be interpreted as infinite expansions “followed by” big bangs, where the cycle renewal “happens” in a mathematical sense: in the way spacetime is metrized. He says that in the infinite future, when all massive particles will have evaporated, we will be returned to a situation without a notion of space or time (since all things are lightlike, I suppose). From this, the very large scale of the given final universe can be reinterpreted as the very small beginning of the next universe. It’s an interesting thought.