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 $|A|\lesssim {10}^{-1}{f}_{NL}$. 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.

• Received 18 May 2013

DOI:https://doi.org/10.1103/PhysRevD.88.083527