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

Abstract

We study the spectrum ${\mathcal{P}}_{\ensuremath{\zeta}}$ and bispectrum ${B}_{\ensuremath{\zeta}}$ of the primordial curvature perturbation $\ensuremath{\zeta}$ 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 ${\mathcal{P}}_{\ensuremath{\zeta}}$ and (or) in ${B}_{\ensuremath{\zeta}}$] and vice versa. The level of non-Gaussianity in the bispectrum, ${f}_{\mathrm{NL}}$, is calculated and related to the level of statistical anisotropy in the power spectrum, ${g}_{\ensuremath{\zeta}}$. 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.