The Primordial Curvature Perturbation from Vector Fields of General non-Abelian Groups

TL;DR

This paper investigates how non-Abelian vector fields can generate primordial curvature perturbations, highlighting their non-Gaussian features, anisotropic bispectrum, and potential observational signatures without conflicting with current anisotropy bounds.

Contribution

It provides a general framework for non-Abelian vector field contributions to curvature perturbations, including bispectrum calculations and an end-of-inflation scenario with observable anisotropy.

Findings

Bispectrum dominated by classical evolution outside the horizon.

Anisotropy in spectrum suppressed by the number of fields.

Large gauge groups can produce observable anisotropy.

Abstract

We consider the generation of primordial curvature perturbation by general non-Abelian vector fields without committing to a particular group. Self-interactions of non-Abelian fields make the field perturbation non-Gaussian. We calculate the bispectrum of the field perturbation using the in-in formalism at tree level. The bispectrum is dominated by the classical evolution of fields outside the horizon. In view of this we show that the dominant contribution can be obtained from the homogeneous classical equation of motion. Then we calculate the power spectrum of the curvature perturbation. The anisotropy in spectrum is suppressed by the number of fields. This makes it possible for vector fields to be responsible for the total curvature perturbation in the Universe without violating observational bounds on statistical anisotropy. The bispectrum of the curvature perturbation is also anisotropic. Finally we give an example of the end-of-inflation scenario in which the curvature perturbation is generated by vector gauge fields through varying gauge coupling constant(s), which in covariant derivatives couples the Higgs field to the vector fields. We find that reasonably large gauge groups may result in the observable anisotropy in the power spectrum of the curvature perturbation.