Non-Gaussianity in multi-field inflation

TL;DR

This work investigates generating primordial non-Gaussianity during inflation without spoiling a nearly scale-invariant adiabatic power spectrum. It identifies a mechanism in two-field inflation where non-Gaussian isocurvature fluctuations, produced naturally by a quartic self-interaction, are transferred to adiabatic perturbations through a bend in the field-space trajectory, with the amount of non-Gaussianity governed by the bending angle Δθ and a single parameter ν3. The authors develop a classical, super-Hubble stochastic treatment to compute the isocurvature PDF and its cumulants, showing that the observable perturbations are a Gaussian part plus a non-Gaussian part of the same variance, with a PDF whose tails can be enhanced or bounded depending on the sign of the quartic coupling. This framework yields clear, testable predictions for CMB and large-scale structure, offering a distinct source of primordial non-Gaussianity that can be distinguished from gravitational non-linearities.

Abstract

This article investigates the generation of non-Gaussianity during inflation. In the context of multi-field inflation, we detail a mechanism that can create significant primordial non-Gaussianities in the adiabatic mode while preserving the scale invariance of the power spectrum. This mechanism is based on the generation of non-Gaussian isocurvature fluctuations which are then transfered to the adiabatic modes through a bend in the classical inflaton trajectory. Natural realizations involve quartic self-interaction terms for which a full computation can be performed. The expected statistical properties of the resulting metric fluctuations are shown to be the superposition of a Gaussian and a non-Gaussian contribution of the same variance. The relative weight of these two contributions is related to the total bending in field space. We explicit the non-Gaussian probability distribution function which appears to be described by a single new parameter. Only two new parameters therefore suffice in describing the non-Gaussianity.

Figures (5)

• Figure 1: The trajectories of the fields in the plane ($\phi,\chi$), once smoothed on a scale $R$. Before Hubble scale crossing ($R<H$), the trajectories behave quantumly because the quantum fluctuations are active up to scale $H$ and are not smoothed out. After the Hubble scale crossing ($R>H$), the trajectories can be treated as classical trajectories. Note that this transition happens at different time for different values of $R$. The bundle of classical trajectories then evolves in the two dimensional potential and its cross section evolves with time. During the bending of the potential valley, the isocurvature modes project on the isocurvature modes and there is a transfer because the length of each trajectory is different depending on its position.
• Figure 2: Diagrammatic representation of the fourth order cumulant in a perturbation theory approach. Lines correspond to connected pair points in ensemble averages of product of Gaussian variables as an application of the Wick theorem. End points are taken at zero order in the coupling constant (they are linear in the initial Gaussian field). Points at first order in the coupling constant are cubic in the field, at second order they are quintic, etc. The first diagram corresponds to the tree order term. It involves only one vertex. The other two diagrams correspond to loop corrections.
• Figure 3: Diagrammatic representation of the sixth order cumulant at leading order. Two types of diagrams appear, one with two three-leg vertices, one with one five-leg vertex.
• Figure 4: Integration path for Eq. (\ref{['pdfexp']}) in the $y$-complex plane (thin solid lines) for $\nu_3\,H^2=0.3$ and ${\underline{\delta}\!s}/{\sigma_s}=0.3$ and $1$. The two half bold lines on the real axis represent the location singularities for $\varphi(y)$. For large values of $\phi$ the integration path is pushed along the singular part (dashed line).
• Figure 5: Shape of the one-point PDF of ${\underline{\delta}\!s}$ for $\nu_3\,H^2=0.3$ (dot-dashed line) or $\nu_3\,H^2=-0.3$ (solid line) compared to a Gaussian distribution (dashed line).