  As a simplest extension to the mass-term curvaton model, the curvaton model
with a polynomial potential can relax the restricted constraint from PLANCK due
to the non-linear dynamics of curvaton field before it decays. We find that
there is still a big room for producing a large negative $g_{\rm NL}$, but not
positive $g_{\rm NL}$. For example, we only need around 10% "tuning" for
$-g_{\rm NL}>10^4$.
