Non-gaussianity from the trispectrum and vector field perturbations

We use the δN formalism to study the trispectrum Tζ of the primordial curvature perturbation ζ when the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, τNL, is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, fNL, and the level of statistical anisotropy in the power spectrum, gζ. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on τNL from WMAP, for generic inflationary models, is done.