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

TL;DR

This paper explores how a pre-inflationary anisotropic phase can leave distinctive non-Gaussian signatures in the cosmological perturbation spectrum, especially in the bi-spectrum, revealing early universe anisotropy effects.

Contribution

It introduces a novel analysis of non-Gaussianities resulting from primordial anisotropy, including effects of higher derivative operators on the bi-spectrum in a single-field inflation model.

Findings

Bi-spectrum is enhanced for flattened and squeezed triangle configurations.

Distinctive angular and momentum dependence of $f_{NL}$ indicates early-time anisotropy.

Early universe anisotropy leaves observable signatures in non-Gaussian features.

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.