Propagation of Gravitational Wave in anIsotropic & Spatially ClosedCosmological Background

In this thesis, we consider a spatially closed FRW universe, in which we study the propagation of gravitational waves. At first, we describe the wave equation in a general curved space-time with a homogeneous matter distribution. After that, we use that wave equation for the spatially closed FRW universe. A key interest of this project is to find an analytic solution for waves in the aforementioned universe. So we consider two different types of matter content. In the first case, the universe expands with constant velocity. In the second case, the universe expands for some time and then collapses after attaining a certain size. We find that for an ever-expanding universe the gravitational waves damp as time flows, and for another case, we observe that for a comoving observer, the amplitude of the gravitational wave decreases while the universe expands and again increases while the universe contracts. The cause behind these types of evolution is also briefly discussed.