On the health of a vector field with (R A^2)/6 coupling to gravity

TL;DR

This paper investigates the stability and physical viability of a vector field coupled to gravity via the (R A^2)/6 term, analyzing its perturbations and energy density to assess potential cosmological implications.

Contribution

It provides the first calculation of energy density from longitudinal perturbations of the vector field and discusses conditions under which the theory remains healthy.

Findings

Longitudinal perturbations contribute finite energy density.

The theory may be stable in certain configurations.

Potential for generating primordial magnetic fields and anisotropic perturbations.

Abstract

The coupling (R A^2)/6 of a vector field to gravity was proposed as a mechanism for generating a primordial magnetic field, and more recently as a mechanism for generating a statistically anisotropic contribution to the primordial curvature perturbation. In either case, the vector field's perturbation has both a transverse and a longitudinal component, and the latter has some unusual features which call into question the health of the theory. We calculate for the first time the energy density generated by the longitudinal field perturbations, and go on to argue that the theory may well be healthy in at least some versions.