Ghosts in classes of non-local gravity

TL;DR

This paper investigates non-local gravity theories, revealing that most auxiliary fields introduced to localize the models are ghost-like, raising concerns about their quantization and physical viability.

Contribution

It provides a detailed analysis of the degrees of freedom in localized non-local gravity models, highlighting the unavoidable presence of ghost-like fields in most cases.

Findings

Most auxiliary fields are ghost-like with negative kinetic energy.

Quantization of these models is problematic due to ghost fields.

A special case without ghosts is identified in the literature.

Abstract

We consider a class of non-local gravity theories where the Lagrangian is a function of powers of the inverse d'Alembertian operator acting on the Ricci scalar. We take an approach in which the non-local Lagrangian is made local by introducing auxiliary scalar fields, and study the degrees of freedom of the localized Lagrangian. We find that among the auxiliary scalar fields introduced, some of them are always ghost-like. That is, in the Einstein frame they develop a negative kinetic term. Because of this, except for a particular case already known in the literature, in general, it is not clear how to quantize these models and how to interpret this theory in the light of standard field theory.