Runnings in the curvaton

Abstract

We investigate the scale-dependence, or the runnings, of linear andsecond order density perturbations generated in various curvatonscenarios. We argue that the second order perturbations,i.e. non-Gaussianity, can strongly depend on the scale, even when thelinear perturbations are nearly scale-invariant. We present analyticformulae for the runnings from curvatons with general energypotentials, and clarify the conditions under which fNLbecomes strongly scale-dependent. From the point of view of thefNL running, curvaton potentials can be classified intoroughly two categories by whether the potential flattens or steepenscompared to a quadratic one. As such examples, we studypseudo-Nambu-Goldstone curvatons, and self-interacting curvatons,respectively. The dynamics of non-quadratic curvatons and thebehaviors of the resulting density perturbations are clarified byanalytical methods.Then we also study models where multiple source can beresponsible for density perturbations such as the multi-curvaton, andmixed curvaton and inflaton models where the running offNL can also be large due to their multi-source nature.We make quantitative analysis for each curvaton scenario and discussin what cases the scale-dependence, in particular, offNL can be large enough to be probed with future CMBexperiments.