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We consider the generation of primordial curvature perturbation by generalnon-Abelian vector fields without committing to a particular group.Self-interactions of non-Abelian fields make the field perturbationnon-Gaussian. We calculate the bispectrum of the field perturbation using thein-in formalism at tree level. The bispectrum is dominated by the classicalevolution of fields outside the horizon. In view of this we show that thedominant contribution can be obtained from the homogeneous classical equationof motion. Then we calculate the power spectrum of the curvature perturbation.The anisotropy in spectrum is suppressed by the number of fields. This makes itpossible for vector fields to be responsible for the total curvatureperturbation in the Universe without violating observational bounds onstatistical anisotropy. The bispectrum of the curvature perturbation is alsoanisotropic. Finally we give an example of the end-of-inflation scenario inwhich the curvature perturbation is generated by vector gauge fields throughvarying gauge coupling constant(s), which in covariant derivatives couples theHiggs field to the vector fields. We find that reasonably large gauge groupsmay result in the observable anisotropy in the power spectrum of the curvatureperturbation.

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