The curvature perturbation in a box

TL;DR

This paper discusses the importance of defining cosmological perturbations, specifically the curvature perturbation, within a finite box to accurately capture their stochastic properties and address related issues.

Contribution

It highlights the necessity of using a finite box for Fourier expansion in analyzing the stochastic properties of curvature perturbations, clarifying conceptual issues.

Findings

Finite box approach clarifies stochastic properties of perturbations

Addresses conceptual issues in defining curvature perturbation

Provides insights into Fourier analysis in cosmology

Abstract

The stochastic properties of cosmological perturbations are best defined through the Fourier expansion in a finite box. I discuss the reasons for that with reference the curvature perturbation, and explore some issues arising from it.