Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy

TL;DR

The paper investigates how a pre-inflationary anisotropic phase leaves imprints on the curvature perturbation spectrum, focusing on high-momentum modes that exit after isotropization. A WKB description in a Kasner-like background is matched to a late-time de Sitter solution, yielding a non-Bunch-Davies vacuum whose anisotropy is encoded in the curvature perturbation's two- and three-point functions. The authors find that anisotropy slightly modifies the power spectrum for certain parameter windows and, more prominently, enhances the bispectrum for flattened and squeezed triangle configurations, with angular dependence reflecting the early-time anisotropy. Introducing a dimension-8 higher-derivative operator amplifies the flattened-triangle signal, potentially reaching observable $f_{NL}$ for sufficiently low cutoff $M$, while squeezed-limit enhancements remain small. Overall, flattened-triangle non-Gaussianity emerges as the dominant anisotropic signature, distinguishing this scenario from generic excited-vacuum models.

Abstract

We investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three-point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon after isotropization. In this momentum regime, the early time dynamics admits a WKB description and the late time dynamics can be described in terms of a non-Bunch Davies vacuum state which encodes the information of initial anisotropy in the background spacetime. We compute the bi-spectrum for curvature perturbation in a canonical single-field action with and without higher derivative operators. We show that the bi-spectrum at late times, in either case, is enhanced for a flattened triangle configuration as well as a squeezed triangle configuration and compute the corresponding $f_{NL}$ parameters. The angular dependence and the particular momentum dependence of the $f_{NL}$ parameter appear as distinctive features of background anisotropy at early times.