Primordial statistical anisotropy generated at the end of inflation

TL;DR

This work introduces a vector field with a non-minimal kinetic term that couples to the waterfall field in a hybrid inflation setup to generate primordial statistical anisotropy. Using the $\delta N$ formalism, the authors show that fluctuations in the end-of-inflation surface, modulated by the vector field, induce direction-dependent curvature perturbations, yielding an anisotropic power spectrum $P_ζ$ and a typically anisotropic bispectrum $B_ζ$. A key result is that the anisotropy can predominantly affect the bispectrum through a shape-dependent $f_{NL}^{ani}$, even when the power-spectrum anisotropy is small, providing a potentially distinctive observational signature. The paper presents explicit formulas for $P_ζ$ and $B_ζ$, analyzes a simple toy model, and discusses the parameter dependence and observational implications, including connections to CMB anomalies and the broader need to consider vector-field effects in early-universe cosmology.

Abstract

We present a new mechanism for generating primordial statistical anisotropy of curvature perturbations. We introduce a vector field which has a non-minimal kinetic term and couples with a waterfall field in hybrid inflation model. In such a system, the vector field gives fluctuations of the end of inflation and hence induces a subcomponent of curvature perturbations. Since the vector has a preferred direction, the statistical anisotropy could appear in the fluctuations. We present the explicit formula for the statistical anisotropy in the primordial power spectrum and the bispectrum of curvature perturbations. Interestingly, there is the possibility that the statistical anisotropy does not appear in the power spectrum but does appear in the bispectrum. We also find that the statistical anisotropy provides the shape dependence to the bispectrum.