Quantifying the behaviour of curvature perturbations near Horizon Crossing

TL;DR

This paper investigates how curvature perturbations evolve after horizon crossing in single field inflation models, revealing significant differences at crossing and quantifying the time needed for perturbations to stabilize.

Contribution

It provides a numerical analysis of curvature perturbation evolution, highlighting the importance of timing when evaluating the power spectrum in inflation models.

Findings

Comoving and uniform density curvature perturbations can differ by up to 180% at horizon crossing.

It takes about 3 e-folds for the curvature perturbation to be within 1% of its final value.

The study emphasizes the need for careful timing in power spectrum evaluation.

Abstract

How much does the curvature perturbation change after it leaves the horizon, and when should one evaluate the power spectrum? To answer these questions we study single field inflation models numerically, and compare the evolution of different curvature perturbations from horizon crossing to the end of inflation. We find that e.g. in chaotic inflation, the amplitude of the comoving and the curvature perturbation on uniform density hypersurfaces differ by up to 180 \% at horizon crossing assuming the same amplitude at the end of inflation, and that it takes approximately 3 efolds for the curvature perturbation to be within 1 \% of its value at the end of inflation.