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