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.
Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA.
Arvind
A
Borde
Alan H
AH
Guth
Alexander
A
Vilenkin