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Primordial non-Gaussianity in warm inflation using $δN$ formalism

A $δN$ formalism is used to study the non-Gaussianity of the primordial curvature perturbation on an uniform density hypersurfaces generated by the warm inflation for the first time. After introducing the framework of the warm inflation and the $δN$ formalism, we obtain an analytic expression for the nonlinear parameter $f_{NL}$ that describes the non-Gaussianity in slow roll approximation, and find that the $δN$ formalism gives a very good result. We analyse the magnitude of $f_{NL}$ and compare our result with those of the standard inflation. Then we discuss two concrete examples: the quartic chaotic model and the hilltop model. The quartic potential model can again be in very good agreement with the Planck results in the warm inflationary scenario, and we give out the concrete results of how the nonlinear parameter depends on the dissipation strength of the warm inflation and the amounts of expansion. We find that the range of the nonlinear parameters in these two cases are both well inside of the allowed region of Planck.