Hemispherical asymmetry and local non-Gaussianity: A consistency condition

Abstract

In this paper we provide a consistency relation between the amplitude of the hemispherical bipolar asymmetry, $A$, and the amplitude of the primordial non-Gaussianity in the squeezed limit, ${f}_{NL}$, as $|A|\ensuremath{\lesssim}{10}^{\ensuremath{-}1}{f}_{NL}$. We demonstrate that this consistency condition is at work for any model of inflation in which the curvature perturbations are sourced by a single light field with the Bunch--Davies initial condition, irrespective of the number of inflation fields that contribute to the background inflationary expansion. As a nontrivial example, we show that observable hemispherical asymmetry can be generated in single-field nonattractor inflationary models. We also study hemispherical asymmetry generated in the models of multiple fields inflation. We show that $A$ is controlled by the weighted sum of non-Gaussianity contribution from each field. In particular, we show that observable hemispherical asymmetry can be generated in models in which inhomogeneities are generated from a light scalar field modulating the surface of the end of inflation.