He reuses a lot of his slides, the one that I have a picture of speaks about taking the boundless expansion and performing an “∞-compression” which I am taking to be a conformal rescaling of the state of the universe at infinity, but I must cede to you that this may be a misunderstanding because he also says on this slide that the Big Bang involves an “∞-expansion” and he certainly doesn't believe that the Big Bang was an infinitely long time ago. In any case what I remember beyond this was that he figured that the expansion at the end of a universe could be used to locate the “cosmic inflation” of a universe _before_ its Big Bang, in the heat death of the prior universe, and it was my impression that it was this “evolution to infinity” of the prior universe but I might be totally mistaken.