Anisotropic Trispectrum of Curvature Perturbations Induced by Primordial Non-Abelian Vector Fields

TL;DR

This paper calculates the anisotropic trispectrum of curvature perturbations in an SU(2) gauge field inflation model, revealing significant anisotropic signatures and contributions from vector fields, extending previous bispectrum analyses.

Contribution

It introduces the calculation of the trispectrum in non-Abelian gauge field inflation models, highlighting the role of gauge self-interactions and anisotropic effects, which were not addressed before.

Findings

Anisotropic signatures in the trispectrum are significant.

Vector field contributions can dominate scalar contributions.

The anisotropic part of the trispectrum can be comparable to the isotropic part.

Abstract

Motivated by the interest in models of the early universe where statistical isotropy is broken and can be revealed in cosmological observations, we consider an SU(2) theory of gauge interactions in a single scalar field inflationary scenario. We calculate the trispectrum of curvature perturbations, as a natural follow up to a previous paper of ours, where we studied the bispectrum in the same kind of models. The choice of a non-Abelian set-up turns out to be very convenient: on one hand, gauge boson self-interactions can be very interesting being responsible for extra non-trivial terms (naturally absent in the Abelian case) appearing in the cosmological correlation functions; on the other hand, its results can be easily reduced to the U(1) case. As expected from the presence of the vector bosons, preferred spatial directions arise and the trispectrum reveals anisotropic signatures. We evaluate its amplitude tau_{NL}, which receives contributions both from scalar and vector fields, and verify that, in a large subset of its parameter space, the latter contributions can be larger than the former. We carry out a shape analysis of the trispectrum; in particular we discuss, with some examples, how the anisotropy parameters appearing in the analytic expression of the trispectrum can modulate its profile and we show that the amplitude of the anisotropic part of the trispectrum can be of the same order of magnitude as the isotropic part.