We investigate the non-Gaussianity of primordial curvature perturbations in the modulated reheating scenario where the primordial perturbation is generated due to the spatial fluctuation of the rate of the inflaton decay to radiation. We use the δN formalism to evaluate the trispectrum of the curvature perturbation as well as its bispectrum. We give expressions for three nonlinear parameters fNL, τNL, and gNL in the modulated reheating scenario. If both the intrinsic non-Gaussianity of scalar field fluctuations and third derivative of the decay rate with respect to the scalar fields are negligibly small, gNL has at least the same order of magnitude as fNL. We also give a general inequality between fNL and τNL, which is true for other inflationary scenarios as long as the primordial non-Gaussianity comes from superhorizon evolution.
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Suyama et al. (2008) studied this question.