One reason people believe in the big bang is that everything is receeding from everything else and if we run time backwards then everything is crunched together. Now the descriptions I've read usually refer to the early universe as a finite space filled with hot gas. My question is, if our current universe is the product of the inflation and then expansion of that early small space then how can it have expanded to the point of being infinite. Does this rule out the possibility of an infinite universe? One slightly related question concerns the CMB. We are bathed in this radiation that was emmited by the universe when it was very uniform and hot. As the universe cooled it presumably stopped radiating as a black body at some point. So will there be a time when all the CMB radiation has passed us by? I havent really thought about the boundry conditions that the CMB radiation would be subject to at the boundry of a finite universe, but if anybody could explain that would be nice. I know there are many models out there, but Im wondering if some are completely eliminated by these considerations.