Three-form inflation and non-Gaussianity

TL;DR

This paper investigates three-form inflation by calculating the perturbed action up to third order, revealing that the spectral index is nearly independent of the potential and exploring non-Gaussianity through bispectrum analysis.

Contribution

It provides a detailed second and third order perturbed action for three-form inflation and explores its observational predictions, including non-Gaussianity, using duality with scalar field theories.

Findings

Spectral index is approximately 0.97, independent of potential.

One model produces large non-Gaussianity.

Results are confirmed via dual scalar field theory.

Abstract

We calculate the perturbed action, at second and third order, for a massive three-form field minimally coupled to gravity, and use it to explore the observational predictions of three-form inflation. One intriguing result is that the value of the spectral index is nearly independent of the three-form potential, being fixed solely by the number of e-folds of inflation, with n_s=0.97 for the canonical number of 60. Considering the bispectrum, we employ standard techniques to give explicit results for two models, one of which produces a large non-Gaussianity. Finally, we confirm our results by employing a duality relating the three-form theory to a non-canonical scalar field theory and explicitly re-computing results in this dual picture.