Non-Gaussianity of the primordial perturbation in the curvaton model

We use the $\ensuremath{\delta}N$ formalism to investigate the non-Gaussianity of the primordial curvature perturbation in the curvaton scenario for the origin of structure. We numerically calculate the full probability distribution function allowing for the noninstantaneous decay of the curvaton and compare this with analytic results derived in the sudden-decay approximation. We also present results for the leading-order contribution to the primordial bispectrum and trispectrum. In the sudden-decay approximation we derive a fully nonlinear expression relating the primordial perturbation to the initial curvaton perturbation. As an example of how non-Gaussianity provides additional constraints on model parameters, we show how the primordial bispectrum on cosmic microwave background scales can be used to constrain variance on much smaller scales in the curvaton field. Our analytical and numerical results allow for multiple tests of primordial non-Gaussianity, and thus they can offer consistency tests of the curvaton scenario.