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.Comment: 18 pages, 12 figures, add new informations in V2, correct some typos
in V
We consider the 3-form field, which has been considered as a candidate for realizing inflation, coupled to a scalar field which models the relativistic matter particles produced during the reheating epoch. We have investigated the stability conditions for this theory and found that introducing such a coupling does not lead to any ghosts or Laplacian instabilities. We have also investigated the reheating temperature and the production of particles due to parametric resonances. We have found that this process is more efficient in this theory compared to the result of the standard-scalar-field inflationary scenario.
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