Anisotropic bispectrum of curvature perturbations from primordial non-Abelian vector fields

TL;DR

This paper investigates how non-Abelian SU(2) gauge fields during inflation induce statistical anisotropy and non-Gaussian features in the curvature perturbations, highlighting the significance of gauge self-interactions in shaping the bispectrum.

Contribution

It introduces a novel calculation of the anisotropic bispectrum from non-Abelian vector fields during inflation, emphasizing the role of gauge self-interactions in generating observable non-Gaussianity.

Findings

The bispectrum peaks in the local configuration.

Gauge self-interactions can dominate the non-Gaussian signal.

Statistical anisotropy modulates the bispectrum amplitude.

Abstract

We consider a primordial SU(2) vector multiplet during inflation in models where quantum fluctuations of vector fields are involved in producing the curvature perturbation. Recently, a lot of attention has been paid to models populated by vector fields, given the interesting possibility of generating some level of statistical anisotropy in the cosmological perturbations. The scenario we propose is strongly motivated by the fact that, for non-Abelian gauge fields, self-interactions are responsible for generating extra terms in the cosmological correlation functions, which are naturally absent in the Abelian case. We compute these extra contributions to the bispectrum of the curvature perturbation, using the delta N formula and the Schwinger-Keldysh formalism. The primordial violation of rotational invariance (due to the introduction of the SU(2) gauge multiplet) leaves its imprint on the correlation functions introducing, as expected, some degree of statistical anisotropy in our results. We calculate the non-Gaussianity parameter f_{NL}, proving that the new contributions derived from gauge bosons self-interactions can be important, and in some cases the dominat ones. We study the shape of the bispectrum and we find that it turns out to peak in the local configuration, with an amplitude that is modulated by the preferred directions that break statistical isotropy.