Viability of vector-tensor theories of gravity

TL;DR

This paper evaluates the viability of vector-tensor gravity theories with a background vector field, identifying stable, ghost-free models that are indistinguishable from General Relativity in local experiments.

Contribution

It classifies vector-tensor theories based on stability, ghost absence, and experimental indistinguishability, highlighting Maxwell-type theories as viable options.

Findings

Six classes of theories are indistinguishable from General Relativity.

Only Maxwell-type and Maxwell with gauge fixing theories are viable.

Conditions for stability and ghost-free behavior are established.

Abstract

We present a detailed study of the viability of general vector-tensor theories of gravity in the presence of an arbitrary temporal background vector field. We find that there are six different classes of theories which are indistinguishable from General Relativity by means of local gravity experiments. We study the propagation speeds of scalar, vector and tensor perturbations and obtain the conditions for classical stability of those models. We compute the energy density of the different modes and find the conditions for the absence of ghosts in the quantum theory. We conclude that the only theories which can pass all the viability conditions for arbitrary values of the background vector field are not only those of the pure Maxwell type, but also Maxwell theories supplemented with a (Lorentz type) gauge fixing term.