Scale dependence of local f_NL

TL;DR

This paper investigates how the non-linearity parameter f_NL, which characterizes primordial non-Gaussianity, can depend on scale in various inflationary models, and discusses potential observability with experiments like Planck.

Contribution

It demonstrates that scale dependence of f_NL is generally first order in slow-roll parameters and identifies conditions under which this dependence could be observed.

Findings

Scale dependence of f_NL is typically first order in slow-roll.

Observable scale dependence may be detectable if f_NL is near current bounds.

Simple quadratic local models predict scale-independent f_NL.

Abstract

We consider possible scale-dependence of the non-linearity parameter f_NL in local and quasi-local models of non-Gaussian primordial density perturbations. In the simplest model where the primordial perturbations are a quadratic local function of a single Gaussian field then f_NL is scale-independent by construction. However scale-dependence can arise due to either a local function of more than one Gaussian field, or due to non-linear evolution of modes after horizon-exit during inflation. We show that the scale dependence of f_NL is typically first order in slow-roll. For some models this may be observable with experiments such as Planck provided that f_NL is close to the current observational bounds.