A semiclassical singularity theorem

TL;DR

This paper derives a new singularity theorem applicable in semiclassical gravity by using quantum energy inequalities, predicting geodesic incompleteness in a toy cosmological model.

Contribution

It introduces a singularity theorem based on quantum energy inequalities, bridging a gap between quantum field theory and classical singularity theorems.

Findings

Predicts timelike geodesic incompleteness in a toy cosmological model

Utilizes quantum energy inequalities for the first time in a singularity theorem

Shows plausibility of singularity formation under semiclassical conditions

Abstract

Quantum fields do not satisfy the pointwise energy conditions that are assumed in the original singularity theorems of Penrose and Hawking. Accordingly, semiclassical quantum gravity lies outside their scope. Although a number of singularity theorems have been derived under weakened energy conditions, none is directly derived from quantum field theory. Here, we employ a quantum energy inequality satisfied by the quantized minimally coupled linear scalar field to derive a singularity theorem valid in semiclassical gravity. By considering a toy cosmological model, we show that our result predicts timelike geodesic incompleteness on plausible timescales with reasonable conditions at a spacelike Cauchy surface.