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arXiv · gr-qc/0110012

Inflationary spacetimes are not past-complete

Arvind Borde·Alan H. Guth·Alexander Vilenkin
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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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Arvind Borde, Alan H. Guth, Alexander Vilenkin. 2003-01-14. Inflationary spacetimes are not past-complete. https://doi.org/10.1103/physrevlett.90.151301

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