A Positive Energy Theorem for P(X,phi) Theories

TL;DR

This paper establishes a positive energy theorem for a class of scalar-tensor theories called P(X,phi), using two independent methods, and explores implications for theories with non-standard dispersion relations.

Contribution

It provides two novel derivations of a positive energy theorem for P(X,phi) theories, extending previous results and allowing for violations of standard dispersion relation assumptions.

Findings

Positive energy can be proven for P(X,phi) theories using auxiliary fields.

Spinorial methods can be directly applied at the P(X,phi) level.

Positive energy results hold even when locality and S-matrix analyticity are violated.

Abstract

We describe a positive energy theorem for Einstein gravity coupled to scalar fields with first-derivative interactions, so-called P(X,phi) theories. We offer two independent derivations of this result. The first method introduces an auxiliary field to map the theory to a lagrangian describing two canonical scalar fields, where one can apply a positive energy result of Boucher and Townsend. The second method works directly at the P(X,phi) level and uses spinorial arguments introduced by Witten. The latter approach follows that of arXiv:1310.1663, but the end result is less restrictive. We point to the technical step where our derivation deviates from theirs. One of the more interesting implications of our analysis is to show it is possible to have positive energy in cases where dispersion relations following from locality and S-Matrix analyticity are violated.