Linear fluctuations in gravity

Abstract

This study investigates gravitational waves as linear perturbations in curved spacetimes. Starting from the linearized Einstein equations, we derive gravitational wave equations in both spatially flat and closed FLRW universes, analyzing their evolution in expanding and contracting scenarios. The study further extends to a five-dimensional anisotropic cosmological model, where gravitational wave behavior is examined using separation of variables and gauge conditions. The results illustrate how spacetime geometry influences wave propagation, offering insights into gravitational dynamics beyond flat backgrounds.