Suppressed non-Gaussianity in the curvaton model

We show that the local type non-Gaussianity in a class of curvaton models is suppressed, i.e., the nonlinearity parameters f(NL) and those related with higher order statistics can be at most O(1), even if the curvaton energy density is subdominant at the decay. This situation is naturally realized in a very simple curvaton potential with quadratic term plus quartic term.