Non-Gaussianity in the modulated reheating scenario

We investigate the non-Gaussianity of primordial curvature perturbation in the modulated reheating scenario where the primordial perturbation is generated due to the spacial fluctuation of the inflaton decay rate to radiation. We use the $\delta N$ formalism to evaluate the trispectrum of curvature perturbation as well as its bispectrum. We give expressions for three non-linear parameters $f_{NL}, \tau_{NL}$ and $g_{NL}$ in the modulated reheating scenario. If the intrinsic non-Gaussianity of scalar field fluctuations and third derivative of the decay rate with respect to scalar fields are negligibly small, $g_{NL}$ has at least the same order of magnitude as $f_{NL}$. We also give general inequality between $f_{NL}$ and $\tau_{NL}$ which is true for other inflationary scenarios as long as primordial non-Gaussianity comes from super-horizon evolution.