Scale dependence of local fNL

We consider possible scale-dependence of the non-linearity parameter fNL 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 fNL 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 fNL is typically first order in slow-roll. For some models this may be observable with experiments such as Planck provided that fNL is close to the current observational bounds.