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Borde-Vilenkin-Guth Theorem ...
"[I]f someone asks me whether or not the theorem I proved with Borde and Guth implies that the universe had a beginning, I would say that the short answer is "yes". If you are willing to get into subtleties, then the answer is "No, but..." So, there are ways to get around having a beginning, but then you are forced to have something nearly as special as a beginning."  Alexander Vilenkin
Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating – or just expanding sufficiently fast – must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.