On Non-Gaussianity in the Curvaton Scenario

TL;DR

Distinguishing curvaton-driven adiabatic perturbations from inflaton-driven ones hinges on non-Gaussianity. The paper develops a fully relativistic, second-order treatment of curvature perturbations on super-horizon scales in a two-fluid curvaton-radiation system, including gravitational corrections, and derives an exact expression for $f_{\rm NL}$ as a function of the transfer parameter $r$. It shows that non-Gaussianity can be enhanced for small $r$ and provides a momentum-dependent component, while in the standard inflaton reheating scenario the second-order curvature perturbation is conserved. These results yield precise, testable predictions for CMB analyses to discriminate early-universe scenarios and guide future observations, with extensions possible to multi-field or inhomogeneous reheating models.

Abstract

Since a positive future detection of non-linearity in the cosmic microwave background anisotropy pattern might allow to descriminate among different mechanisms giving rise to cosmological adiabatic perturbations, we study the evolution of the second-order cosmological curvature perturbation on super-horizon scales in the curvaton scenario. We provide the exact expression for the non-Gaussianity in the primordial perturbations including gravitational second-order corrections which are particularly relevant in the case in which the curvaton dominates the energy density before it decays. As a byproduct, we show that in the standard scenario where cosmological curvature perturbations are induced by the inflaton field, the second-order curvature perturbation is conserved even during the reheating stage after inflation.