Nonlinear curvature perturbations in an exactly soluble model of multi-component slow-roll inflation

TL;DR

The paper addresses non-Gaussianity in curvature perturbations from multi-component slow-roll inflation by presenting an exactly solvable model with $V(\boldsymbol{\phi}) = V_0 \exp\left[\frac{1}{2}\sum_A m_A^2 \phi_A^2\right]$ and ending inflation via a waterfall on a deformed-sphere surface. Using the $δN$ formalism, it derives an analytic expression for the nonlinear curvature perturbation through $N(\boldsymbol{\phi})$ and its derivatives, enabling evaluation of the linear spectrum and the level of non-Gaussianity. The study finds that the linear spectrum is $P_S$ determined by $\sum_A (\partial N/\partial \phi_A)^2$, the tensor-to-scalar ratio is inversely related to this sum, and higher-order non-Gaussian terms are suppressed unless slow-roll is violated or post-inflationary physics contributes. This work provides a tractable benchmark clarifying how multi-field slow-roll dynamics constrain non-Gaussianity and guides analytic investigations of primordial curvature perturbations.

Abstract

Using the nonlinear $δN$ formalism, we consider a simple exactly soluble model of multi-component slow-roll inflation in which the nonlinear curvature perturbation can be evaluated analytically.