The hemispherical asymmetry from a scale-dependent inflationary bispectrum

Abstract

If the primordial bispectrum is sufficiently large then the CMB hemispherical power asymmetry may be explained by a large-scale mode of exceptional amplitude which perturbs the ζ two-point function. We extend previous calculations, which were restricted to one- or two-source scenarios, by providing a method to compute the response of the two-point function in any model yielding a 'local-like' bispectrum. In general, this shows that it is not the reduced bispectrum fNL(k1, k2, k3) which sources the amplitude and scale-dependence of the mode coupling but rather a combination of 'response functions'. We discuss why it is difficult to construct successful scenarios and enumerate the fine-tunings which seem to be required. Finally, we exhibit a concrete model which can be contrived to match the observational constraints and show that to a Planck-like experiment it would appear to have |NLlocal| ∼ |NLequi| ∼ |NLortho| ≤ 1. Therefore, contrary to previous analyses, we conclude that it is possible to generate the asymmetry while respecting observational constraints on the bispectrum and low-ℓ multipoles even without tuning our location on the long-wavelength mode.