On the perturbation theory in spatially closed background

Abstract

In this article, we investigate some features of the perturbation theory in a 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 much longer than the Hubble horizon. It will be revealed that these adiabatic solutions do not depend on the curvature directly. We also propose a new interpretation for the curvature perturbation in terms of the unperturbed background geometry.