Stability of the 3-form field during inflation
  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. 
Antonio De Felice, Khamphee Karwan, Pitayuth Wongjun
hep-ph astro-ph.CO gr-qc