Anisotropic non-Gaussianity from vector field perturbations

TL;DR

This work analyzes how vector-field perturbations can imprint anisotropic non-Gaussianity in the primordial curvature perturbation $\zeta$ through the $\delta N$ formalism. It derives general expressions for the anisotropic bispectrum and $f_{NL}$, showing explicit orientation dependence via $A_{\perp}$ and linking $f_{NL}$ to the power-spectrum anisotropy parameter $g$. The paper then examines two concrete models—the vector curvaton (including a non-minimally coupled case) and anisotropy generated at the end of inflation—providing explicit $f_{NL}^{\mathrm{equil}}$ and $f_{NL}^{\mathrm{local}}$ formulas that scale with $g$ (often as $g^{2}$) and with other model parameters. It discusses observational prospects, constraints, and the need for broader theoretical tools to fully exploit potential anisotropic signatures as smoking-gun evidence for vector-field contributions to $\zeta$.

Abstract

We suppose that a vector field perturbation causes part of the primordial curvature perturbation. The non-Gaussianity parameter fNL is then, in general, statistically anisotropic. We calculate its form and magnitude in the curvaton scenario and in the end-of-inflation scenario. We show that this anisotropy could easily be observable.