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 jAj & 10 À1 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.

CMB hemispherical asymmetry: long mode modulation and non-Gaussianity

“…In this note we show that there is no inconsistency in [17,18] and the results in [17,18] make sense both mathematically and conceptually. In turn, we also comment on the logic of [1] in relating the observed dipole asymmetry to equilateral configurations.…”

“…This kind of modulation can lead to an asymmetry as studied in [13,14,15,16]. In [17] we have shown that such a modulation is due to a non-linear correlation between the long mode and small CMB modes, i.e. the squeezed limit non-Gaussianity.…”

“…Eq. (7) is the consistency relation obtained in [17] which clearly shows that the amplitude of dipole asymmetry is controlled by the squeezed limit non-Gaussianity. Note again that f NL here can be scale-dependent which can be used to explain the scale-dependent dipole asymmetry as required by the lack of any dipole asymmetry on ℓ > 600 [9,10].…”

“…Let us now review our approach in [17,18] in providing the relation between the squeezed limit non-Gaussianity and the amplitude of dipole asymmetry. In doing so we also answer the criticisms raised in [1] and confirm our approach in [17,18].…”

“…Recently the paper [1] appeared in which the author criticized our approach employed in [17,18] to obtain a consistency relation between the amplitude of dipole asymmetry and the squeezed limit non-Gaussianity. In this note we show that there is no inconsistency in [17,18] and the results in [17,18] make sense both mathematically and conceptually.…”