Anisotropic Non-Gaussianity from a Two-Form Field

TL;DR

This paper explores an inflationary model with a two-form field that induces statistical anisotropy in the curvature perturbations, analyzing its non-Gaussian features and consistency with observational bounds.

Contribution

It demonstrates that anisotropic inflation driven by a two-form field can produce distinctive non-Gaussian signatures and remains consistent with current observational constraints.

Findings

Anisotropic inflation with a two-form field is an attractor solution.

The power spectrum exhibits prolate-type anisotropy.

Non-Gaussianity parameters $f_{NL}$ and $ au_{NL}$ are correlated with the anisotropy amplitude.

Abstract

We study an inflationary scenario with a two-form field to which an inflaton couples non-trivially. First, we show that anisotropic inflation can be realized as an attractor solution and that the two-form hair remains during inflation. A statistical anisotropy can be developed because of a cumulative anisotropic interaction induced by the background two-form field. The power spectrum of curvature perturbations has a prolate-type anisotropy, in contrast to the vector models having an oblate-type anisotropy. We also evaluate the bispectrum and trispectrum of curvature perturbations by employing the in-in formalism based on the interacting Hamiltonians. We find that the non-linear estimators $f_{NL}$ and $\tau_{NL}$ are correlated with the amplitude $g_*$ of the statistical anisotropy in the power spectrum. Unlike the vector models, both $f_{NL}$ and $\tau_{NL}$ vanish in the squeezed limit. However, the estimator $f_{NL}$ can reach the order of 10 in the equilateral and enfolded limits. These results are consistent with the latest bounds on $f_{NL}$ constrained by Planck.