Quantifying the behaviour of curvature perturbations during inflation

TL;DR

This paper investigates how curvature perturbations evolve during inflation, determining the number of efolds needed for these perturbations to stabilize, which informs the correct timing for power spectrum evaluation.

Contribution

It provides a numerical analysis of curvature perturbation evolution during inflation, quantifying the time needed for perturbations to settle and highlighting differences at horizon crossing.

Findings

Curvature perturbations differ by up to 180% at horizon crossing.

Approximately 3 efolds are needed for perturbations to be within 1% of their final value.

The study offers guidance on when to evaluate the power spectrum during inflation.

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. In particular we calculate the number of efolds it takes for the curvature perturbation at a given wavenumber to settle down to within a given fraction of their value at 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.