Non-Gaussianities of Single Field Inflation with Non-minimal Coupling

TL;DR

This paper studies the non-Gaussian features in single-field inflation models with non-minimal coupling, analyzing how the shape and amplitude of the 3-point correlation depend on model parameters and providing numerical results for specific inflation scenarios.

Contribution

It introduces a parameter relating slow-roll parameters to analyze non-Gaussianities in non-minimally coupled inflation, and explores the shape dependence and numerical predictions of the 3-point function.

Findings

Dependence of 3-point correlation shape on the parameter μ.

Expression for the estimator F_NL in the equilateral limit.

Numerical results for non-Gaussianities in non-minimal chaotic inflation.

Abstract

We investigate the non-Gaussianities of inflation driven by a single scalar field coupling non-minimally to the Einstein Gravity. We assume that the form of the scalar field is very general with an arbitrary sound speed. For convenience to study, we take the subclass that the non-minimal coupling term is linear to the Ricci scalar $R$. We define a parameter $\mu\equiv\epsilon_h/\epsilon_\theta$ where $\epsilon_h$ and $\epsilon_\theta$ are two kinds of slow-roll parameters, and obtain the dependence of the shape of the 3-point correlation function on $\mu$. We also show the estimator $F_{NL}$ in the equilateral limit. Finally, based on numerical calculations, we present the non-Gaussianities of non-minimal coupling chaotic inflation as an explicit example.