Non-linear inflationary perturbations

TL;DR

This work develops a non-linear, gauge-invariant framework for studying inflationary perturbations in single- and multi-field models within a long-wavelength gradient expansion. It introduces non-linear generalizations of Sasaki-Mukhanov variables $\mathcal{Q}^A_i$ whose evolution is governed by a closed equation with a mass matrix $\Omega^A{}_B$, coupled to stochastic noise that seeds initial conditions after horizon crossing; this enables fully non-linear evolution on superhorizon scales while allowing arbitrary time-slicing. The approach unifies the treatment of adiabatic and isocurvature perturbations, provides a practical path for numerical simulations, and targets the computation of primordial non-Gaussianity in realistic inflationary scenarios. The framework offers a powerful tool for making quantitative predictions that can be tested with upcoming CMB and large-scale structure observations, helping to discriminate between competing inflationary models.

Abstract

We present a method by which cosmological perturbations can be quantitatively studied in single and multi-field inflationary models beyond linear perturbation theory. A non-linear generalization of the gauge-invariant Sasaki-Mukhanov variables is used in a long-wavelength approximation. These generalized variables remain invariant under time slicing changes on long wavelengths. The equations they obey are relatively simple and can be formulated for a number of time slicing choices. Initial conditions are set after horizon crossing and the subsequent evolution is fully non-linear. We briefly discuss how these methods can be implemented numerically in the study of non-Gaussian signatures from specific inflationary models.