Inflationary spacetimes are not past-complete

  title={Inflationary spacetimes are not past-complete},
  author={A. H. de Borde and Alan Harvey Guth and Alexander Vilenkin},
  journal={Physical Review Letters},
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… 

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