Non-gaussianity in curvaton models with nearly quadratic potentials

We consider curvaton models with potentials that depart slightly from the quadratic form. We show that although such a small departure does not significantly modify the Gaussian part of the curvature perturbation, it can have a pronounced effect on the level of non-Gaussianity. We. find that unlike in the quadratic case, the limit of small non-Gaussianity, vertical bar fNL vertical bar << 1, is quite possible even with small curvaton energy density r << 1. Furthermore, non-Gaussianity does not imply any strict bounds on r, but the bounds depend on the assumptions about the higher order terms in the curvaton potential.