Inflationary spacetimes are not past-complete

TL;DR

This paper demonstrates that inflationary spacetimes are necessarily past-incomplete without relying on energy conditions, implying the need for new physics to describe their origins.

Contribution

It provides a simple kinematical argument showing inflationary models are past-incomplete without assuming energy conditions.

Findings

Inflationary spacetimes are past-incomplete in null and timelike directions.

A bound on the integral of the Hubble parameter is derived.

Inflation models require physics beyond inflation to explain their past boundary.

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.