Instability of the ACW model, and problems with massive vectors during inflation

TL;DR

This paper demonstrates that the Ackerman-Carroll-Wise (ACW) anisotropic inflation model with a fixed-norm vector field is fundamentally unstable due to ghost instabilities, raising concerns about its viability and quantum consistency.

Contribution

The paper provides a detailed stability analysis of the ACW model and related vector field models, revealing inherent ghost instabilities and their implications for inflationary cosmology.

Findings

The ACW model's background is unstable due to ghost perturbations.

Vector field models with wrong-sign mass terms have longitudinal ghosts.

Ghosts pose challenges for quantum consistency and UV completion.

Abstract

We prove that the anisotropic inflationary background of the Ackerman-Carroll-Wise model, characterized by a fixed-norm vector field, is unstable. We found the instability by explicitly solving the linearized equations for the most general set of perturbations around this background, and by noticing that the solutions diverge close to horizon crossing. This happens because one perturbation becomes a ghost at that moment. A simplified computation, with only the perturbations of the vector field included, shows the same instability, clarifying the origin of the problem. We then discuss several other models, with a particular emphasis on the case of a nonminimal coupling to the curvature, in which vector fields are used either to support an anisotropic expansion, or to generate cosmological perturbations on an isotropic background. In many cases, the mass term of the vector needs to have the ``wrong'' sign; we show that, as a consequence, the longitudinal vector mode is a ghost (a field with negative kinetic term, and negative energy; not simply a tachyon). We comment on problems that arise at the quantum level. In particular, the presence of a ghost can be a serious difficulty for the UV completion that such models require in the sub-horizon regime.