Inflationary spacetimes are incomplete in past directions |
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Authors: | Borde Arvind Guth Alan H Vilenkin Alexander |
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Institution: | Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA. |
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Abstract: | 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. |
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