Inflationary Spacetimes Are Incomplete in Past Directions
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 pastdirected timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.
 Publication:

Physical Review Letters
 Pub Date:
 April 2003
 DOI:
 10.1103/PhysRevLett.90.151301
 arXiv:
 arXiv:grqc/0110012
 Bibcode:
 2003PhRvL..90o1301B
 Keywords:

 98.80.Cq;
 04.20.Dw;
 Particletheory and fieldtheory models of the early Universe;
 Singularities and cosmic censorship;
 General Relativity and Quantum Cosmology
 EPrint:
 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