Modave lectures on energy conditions in quantum field theory and semi-classical gravity

TL;DR

This paper reviews classical and quantum energy conditions in gravity, discussing their implications, violations, and bounds in quantum field theories coupled to gravity, with insights into quantum gravity.

Contribution

It provides a comprehensive overview of energy conditions in quantum field theory and semi-classical gravity, highlighting recent bounds and their implications for quantum gravity.

Findings

Classical energy conditions underpin singularity theorems.

Quantum fields violate local energy conditions.

Bounds on energy densities relate to quantum information.

Abstract

We review well known classical energy conditions and their implications for gravitational solutions, including the celebrated Hawking and Penrose singularity theorems. We then consider quantum fields coupled to gravity, where the topic becomes both richer and more subtle, as even the simplest quantum theories violate local energy conditions. We discuss directions for constraining energy densities in quantum field theories, including averaging over regions of spacetime and bounds relating energy and quantum information. We explore implications of these bounds for quantum field theory coupled to gravity as an effective theory and discuss how they guide our understanding of quantum gravity more broadly. These notes are based on a series of lectures given at the XXI Modave Summer School in Mathematical Sciences.