Stability of the 3-form field during inflation

TL;DR

This paper investigates the stability conditions of a 3-form field during inflation, proposing new potential classes that ensure stability, slow-roll inflation, and potential non-Gaussianities in primordial perturbations.

Contribution

It identifies unstable potentials like the Mexican-hat and introduces stable alternatives that support inflation and non-Gaussianity potential.

Findings

Certain potentials are unstable due to ghosts and Laplacian instabilities.

New stable potentials support slow-roll inflation and oscillatory epochs.

Some models predict small propagation speeds, allowing non-Gaussianities.

Abstract

We consider the minimally coupled 3-form field which has been considered as a candidate to realize inflation. We have studied the conditions to avoid ghosts and Laplacian instabilities and found that some classes of potentials, e.g. the Mexican-hat one, will in general be unstable. We then propose other classes of potentials which are instead free from any instability, drive a long-enough slow-roll regime followed by an oscillatory epoch, and as a consequence, can provide successful inflation. Finally, we also provide stable potentials which lead to a small enough propagation speed for the scalar perturbations, giving a possibility for these models to produce non-Gaussianities.