Phys. Rev. Lett. 90, 151301 (2003) [4 pages]Inflationary Spacetimes Are Incomplete in Past DirectionsReceived 5 October 2001; revised 24 January 2003; published 15 April 2003 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. © 2003 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.90.151301
DOI:
10.1103/PhysRevLett.90.151301
PACS:
98.80.Cq, 04.20.Dw
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