We present a systematic study of the amplitude of the primordial perturbation in curvaton models with self-interactions, treating both renormalizable and non-renormalizable interactions. In particular, we consider the possibility that the curvaton energy density is subdominant at the time of the curvaton decay. We find that large regions in the parameter space give rise to the observed amplitude of primordial perturbation even for non-renormalizable curvaton potentials, for which the curvaton energy density dilutes fast. At the time of its decay, the curvaton energy density may typically be subdominant by a relative factor of 10 −3 and still produce the observed perturbation. Field dynamics turns out to be highly non-trivial, and for non-renormalizable potentials and certain regions of the parameter space we observe a non-monotonous relation between the final curvature perturbation and the initial curvaton value. In those cases, the time evolution of the primordial perturbation also displays an oscillatory behaviour before the curvaton decay.

There are observations of at least 15 high-redshift massive galaxy clusters, which have an extremely small probability with a purely Gaussian initial curvature perturbation. Here we revisit the estimation of the contribution of non-Gaussianities to the cluster mass function and point out serious problems that have resulted from the application of the mass function out of the range of its validity. We remedy the situation and show that the values of f NL previously claimed to completely reconcile (i.e. at ∼ 100% confidence) the existence of the clusters with ΛCDM are unphysically small. However, for WMAP cosmology and at 95% confidence, we arrive at the limit f NL 411, which is similar to previous estimates. We also explore the possibility of a large g NL as the reason for the observed excess of the massive galaxy clusters. This scenario, g NL > 2 × 10 6 , appears to be in more agreement with CMB and LSS limits for the non-Gaussianity parameters and could also provide an explanation for the overabundance of large voids in the early universe.

We investigate non-Gaussianities in self-interacting curvaton models treating both renormalizable and non-renormalizable polynomial interactions. We scan the parameter space systematically and compute numerically the non-linearity parameters f NL and g NL . We find that even in the interaction dominated regime there are large regions consistent with current observable bounds. Whenever the interactions dominate, we discover significant deviations from the relations f NL ∼ r −1 dec and g NL ∼ r −1 dec valid for quadratic curvaton potentials, where r dec measures the curvaton contribution to the total energy density at the time of its decay. Even if r dec ≪ 1, there always exists regions with f NL ∼ 0 since the sign of f NL oscillates as a function of the parameters. While g NL can also change sign, typically g NL is non-zero in the low-f NL regions. Hence, for some parameters the non-Gaussian statistics is dominated by g NL rather than by f NL . Due to self-interactions, both the relative signs of f NL and g NL and the functional relation between them is typically modified from the quadratic case, offering a possible experimental test of the curvaton interactions. Non-Gaussianities in self-interacting curvaton modelsWe use the δN formalism [14,15] and assume that the curvature perturbation arises solely from perturbations of a single curvaton field generated during inflation. The