Hemispherical asymmetry and local non-Gaussianity: A consistency condition

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 vertical bar A vertical bar less than or similar to 10(-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.