Non-gaussianity from the trispectrum and vector field perturbations

Abstract

We use the δN formalism to study the trispectrum T_ζof the primordial curvature perturbation ζwhen 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, τ_{NL}, is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f_{NL}, and the level of statistical anisotropy in the power spectrum, g_ζ. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on τ_{NL} from WMAP, for generic inflationary models, is done.

LaTeX file, 12 pages, no figures. v2: Minor changes, conclusions unchanged. v3: Version accepted for publication in Physics Letters B