Non-minimal coupling, negative null energy, and effective field theory

TL;DR

This paper argues that non-minimal scalar-gravity couplings, viewed through an effective field theory lens, do not violate the null energy condition, thus challenging claims of exotic phenomena like traversable wormholes.

Contribution

It demonstrates that within an EFT framework, the null energy condition holds, and introduces a smeared null energy condition dependent on the field range.

Findings

Null energy condition is obeyed in non-minimal coupling EFTs.

A state-dependent bound on smeared null energy is established.

Classical and quantum analyses show no violation of energy conditions.

Abstract

The non-minimal coupling of scalar fields to gravity has been claimed to violate energy conditions, leading to exotic phenomena such as traversable wormholes, even in classical theories. In this work we adopt the view that the non-minimal coupling can be viewed as part of an effective field theory (EFT) in which the field value is controlled by the theory's cutoff. Under this assumption, the average null energy condition, whose violation is necessary to allow traversable wormholes, is obeyed both classically and in the context of quantum field theory. In addition, we establish a type of "smeared" null energy condition in the non-minimally coupled theory, showing that the null energy averaged over a region of spacetime obeys a state dependent bound, in that it depends on the allowed field range. We finally motivate our EFT assumption by considering when the gravity plus matter path integral remains semi-classically controlled.