Non-Gaussianity in multiple three-form field inflation

TL;DR

This paper develops a method using the $ abla N$ formalism to analyze primordial non-Gaussianity in multiple three-form field inflation, linking three-form fields to scalar fields and calculating the bispectrum.

Contribution

It introduces a novel approach to compute the bispectrum in three-form inflation models, extending the $ abla N$ formalism to this context and providing explicit expressions for observational predictions.

Findings

Bispectrum amplitude in equilateral and orthogonal configurations is of order 1.

Squeezed limit bispectrum amplitude is around 10^{-3}.

Model is consistent with current observational constraints.

Abstract

In this work, we present a method for implementing the $\delta N$ formalism to study the primordial non-Gaussianity produced in multiple three-form field inflation. Using a dual description relating three-form fields to noncanonical scalar fields, and employing existing results, we produce expressions for the bispectrum of the curvature perturbation in terms of three-form quantities. We study the bispectrum generated in a two three-form field inflationary scenario for a particular potential that for suitable values of the parameters was found in earlier work to give values of the spectral index and ratio of tensor to scalar perturbations compatible with current bounds. We calculate the reduced bispectrum for this model, finding an amplitude in equilateral and orthogonal configurations of ${\cal O}(1)$ and in the squeezed limit of ${\cal O}(10^{-3})$. We confirm, therefore, that this three-form inflationary scenario is compatible with present observational constraints.