Non-Gaussianity at tree and one-loop levels from vector field perturbations

We study the spectrum P_ζ and bispectrum B_ζ of the primordial curvature perturbation ζ when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree-level terms [both (either) in P_ζ and (or) in B_ζ] and vice versa. The level of non-Gaussianity in the bispectrum, fNL, is calculated and related to the level of statistical anisotropy in the power spectrum, g_ζ. For very small amounts of statistical anisotropy in the power spectrum, the level of non-Gaussianity may be very high, in some cases exceeding the current observational limit.