Super-Hubble Nonlinear Perturbations During Inflation

TL;DR

This paper develops an exact solution for the nonlinear evolution of super-Hubble perturbations during inflation, showing their limited amplification during reheating and implications for back-reaction and vector mode generation.

Contribution

It introduces a first-order gradient expansion solution for nonlinear super-Hubble perturbations, clarifying their behavior and effects in inflationary scenarios.

Findings

No parametric amplification of super-Hubble modes during reheating in single-field models

Long wavelength vector modes are generated if slow-roll conditions are violated

Provides a new derivation of the stochastic inflation equation of motion

Abstract

We show that the non-linear evolution of long wavelength perturbations may be important in a wide class of inflationary scenarios. We develop a solution for the evolution of such nonlinear perturbations which is exact to first order in a gradient expansion. As a first application, we demonstrate that in single field models of inflation there can be no parametric amplification of super-Hubble modes during reheating. We consider the implications of the solution for recent discussions of the back-reaction effect of long wavelength perturbations on the background geometry, give a new derivation of the equation of motion of stochastic inflation, and demonstrate that if the (generalized) slow-rolling condition is not satisfied, then inevitably long wavelength vector modes for gravitational fluctuations will be generated.