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

We study the spectrum Pζ and bispectrum Bζ 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 Pζ and (or) in Bζ] 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, gζ. 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.