Hemispherical Asymmetry and Local non-Gaussianity: a Consistency Condition

TL;DR

This paper establishes a consistency relation linking hemispherical asymmetry amplitude and primordial non-Gaussianity, applicable across various inflation models, and explores conditions under which observable asymmetry can arise.

Contribution

It derives a universal consistency condition between hemispherical asymmetry and non-Gaussianity in single and multi-field inflation models, including non-attractor scenarios.

Findings

The relation |A|  10^{-1} f_{NL} holds generally.

Observable asymmetry can occur in single-field non-attractor models.

Multi-field models show asymmetry controlled by a weighted sum of contributions.

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 $|A| \lesssim 10^{-1} f_{NL}$. We demonstrate that this consistency condition is at work for any model of inflation in which the curvature perturbations is sourced by a single light field with the Bunch-Davies initial condition, irrespective of the number of inflation fields which contribute to the background inflationary expansion. As a non-trivial example, we show that observable hemispherical asymmetry can be generated in single field non-attractor 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 where inhomogeneities are generated from a light scalar field modulating the surface of end of inflation.