The self-interacting curvaton

The evolution of the curvature perturbation is highly non-trivial for curvaton models with self-interactions and is very sensitive to the parameter values. The final perturbation depends also on the curvaton decay rate $\Gamma$. As a consequence, non-gaussianities can be greatly different from the purely quadratic case, even if the deviation is very small. Here we consider a class of polynomial curvaton potentials and discuss the dynamical behavior of the curvature perturbation. We point out that, for example, it is possible that the non-gaussianity parameter $\fnl\simeq 0$ while $\gnl$ is non-zero. In the case of a curvaton with mass $m\sim {\cal O}(1)$ TeV we show that one cannot ignore non-quadratic terms in the potential, and that only a self-interaction of the type $V_{\rm int}=\sigma^8/M^4$ is consistent with various theoretical and observational constraints. Moreover, the curvaton decay rate should then be in the range $\Gamma=10^{-15}- 10^{-17}$ GeV.