On the perturbation theory in spatially closed background

TL;DR

This paper explores the characteristics of perturbation theory in a spatially closed universe, revealing the existence of two adiabatic solutions for long-wavelength modes and offering a new interpretation of curvature perturbation.

Contribution

It demonstrates that perturbative equations in a closed universe always have two adiabatic solutions for long wavelengths, independent of curvature, and proposes a novel interpretation of curvature perturbation.

Findings

Two independent adiabatic solutions for long-wavelength perturbations.

Adiabatic solutions are curvature-independent.

New interpretation of curvature perturbation in unperturbed geometry.

Abstract

In this article,we investigate some features of the perturbation theory in spatially closed universe. We will show that the perturbative field equations in a spatially closed universe always have two independent adiabatic solutions provided that the wavelengths of perturbation modes are very longer than the Hubble horizon. It will be revealed that these adiabatic solutions do not depend on the curvature directly. We also propound a new interpretation for the curvature perturbation in terms of the unperturbed geometry.