The primordial curvature perturbation from vector fields of generalnon-Abelian groups

Abstract

We consider the generation of primordial curvature perturbation bygeneral non-Abelian vector fields without committing to a particulargroup. Self-interactions of non-Abelian fields make the fieldperturbation non-Gaussian. We calculate the bispectrum of the fieldperturbation using the in-in formalism at tree level. The bispectrumis dominated by the classical evolution of fields outside the horizon.In view of this we show that the dominant contribution can be obtainedfrom the homogeneous classical equation of motion. Then we calculatethe power spectrum of the curvature perturbation. The anisotropy inspectrum is suppressed by the number of fields. This makes it possiblefor vector fields to be responsible for the total curvature perturbationin the Universe without violating observational bounds on statisticalanisotropy. The bispectrum of the curvature perturbation is also anisotropic.Finally we give an example of the end-of-inflation scenario in whichthe curvature perturbation is generated by vector gauge fields throughvarying gauge coupling constant(s), which in covariant derivativescouples the Higgs field to the vector fields. We find that reasonablylarge gauge groups may result in the observable anisotropy in thepower spectrum of the curvature perturbation.