Signatures of non-Gaussianity in the curvaton model

We discuss the signatures of non-Gaussianity in the curvaton model where the potential includes also a non-quadratic term. In such a case the non-linearity parameter f(NL) can become very small, and we show that non-Gaussianity is then encoded in the non-reducible non-linearity parameter gNL of the trispectrum, which can be very large. Thus the place to look for the non-Gaussianity in the curvaton model may be the trispectrum rather than the bispectrum. We also show that gNL measures directly the deviation of the curvaton potential from the purely quadratic form. While gNL depends on the strength of the non-quadratic terms relative to the quadratic one, we find that for reasonable cases roughly gNL similar to O(-10(4))-O(-10(5)), which are values that may well be accessible by future observations.