Inflationary spacetimes are not past-complete
General Relativity and Quantum Cosmology
2009-11-07 v2
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.
Keywords
Cite
@article{arxiv.gr-qc/0110012,
title = {Inflationary spacetimes are not past-complete},
author = {Arvind Borde and Alan H. Guth and Alexander Vilenkin},
journal= {arXiv preprint arXiv:gr-qc/0110012},
year = {2009}
}
Comments
We improve the basic argument to apply to a wider class of spacetimes, use a better title and add a discussion of cyclic models. 4 pages, 1 figure, RevTeX