Accurately determining inflationary perturbations

Abstract

Cosmic microwave anisotropy satellites promise extremely accurate measures of the amplitude of perturbations in the universe. We use a numerical code to test the accuracy of existing approximate expressions for the amplitude of perturbations produced by single-field inflation models. We find that the second-order Stewart-Lyth calculation gives extremely accurate results, typically better than one percent. We use our code to carry out an expansion about the general power-law inflation solution, providing a fitting function giving results of even higher accuracy.