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