Higher order statistics of curvature perturbations in IFF model and its Planck constraints

We compute the power spectrum P_\zeta, and non-linear parameters f_nl and \tau_nl of the curvature perturbation induced during inflation by the electromagnetic fields in the kinetic coupling model (IFF model). By using the observational result of P_\zeta, f_nl and \tau_nl reported by the Planck collaboration, we study the constraint on the model comprehensively. Interestingly, if the single slow-rolling inflaton is responsible for the observed P_\zeta, the constraint from \tau_nl is most stringent. We also find a general relationship between f_nl and \tau_nl generated in this model. Even if f_nl \sim O(1), a detectable \tau_nl can be produced.