Non-linear isocurvature perturbations and non-Gaussianities

TL;DR

This paper develops an extended $\delta N$ formalism to describe non-linear primordial perturbations that include both adiabatic and isocurvature components. It applies the framework to two multi-field inflation setups: a mixed inflaton-curvaton model and a double inflation model with two massive fields, deriving how the final curvature and isocurvature perturbations, as well as their bispectra, depend on initial field fluctuations. A key finding is that the isocurvature bispectrum can be large when the inflaton dominates the linear spectrum and the CDM is generated by curvaton decay, though observational constraints on isocurvature power bound the overall amplitude. In the double inflation scenario, non-linearities are generally slow-roll suppressed, yielding small non-Gaussianities, while still allowing for potential isocurvature-adiabatic correlations in more general two-field models. These results provide a framework for testing multi-field inflation with upcoming CMB data by linking non-linear perturbations to the underlying field dynamics.

Abstract

We study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended delta N-formalism, we analyse in detail two illustrative examples. The first is a mixed curvaton-inflaton scenario in which fluctuations of both the inflaton and a curvaton (a light isocurvature field during inflation) contribute to the primordial density perturbation. The second example is that of double inflation involving two decoupled massive scalar fields during inflation. In the mixed curvaton-inflaton scenario we find that the bispectrum of primordial isocurvature perturbations may be large and comparable to the bispectrum of adiabatic curvature perturbations.