Without inflation, only extremely special conditions in the past produce the universe we now see. Or so the story goes. Penrose has long argued that conditions necessary for inflation are actually more special that the necessary past conditions without inflation. Its seems that Sean Carroll agrees with this (slides 15 and 16). Carroll seems to prefer a multiverse explanation over inflation. I think, however, that Penrose (nay) and Carroll (yeah) disagree on the likelihood that inflation happened, and that Penrose's position is quite non-standard. Note that the questions of 1) the specialness of necessary conditions for inflation and 2) physical evidence that inflation occurred, are quite different. Also note that in his GR book, Carroll does not mention that special conditions are necessary for inflation, so maybe: I have misinterpreted Carroll; Carroll has thought about this since writing his GR book; Carroll thought that this was a little too speculative for his GR book; or ..., etc.