Non-Gaussianities of single field inflation with nonminimal coupling

Abstract

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