Randall-sundrum Membrane Model And Its Instability Study

There have been enormous interests in the brane world theories recently. After reviewing the brane theories in detail, the instability of the Randall-Sundrum brane model and quantum effects of an extra compact dimension have been discussed in this thesis. Five diensional geodesic equation is used to study the gravitational force acted on a test particle in the bulk of the Randall-Sundrum two-brane model. It is this force that causes the model to be unstable. So a 5D fluid is introduced to balance the gravity from the two branes. And a class of exact bulk solutions is obtained. By requiring a 4D effective curvature to have a minimum, the compactification size of the extra dimension is discussed. In order to study the quantum effects of an extra dimension, a Hamiltonian formulation for a 5D FRW cosmology is derived through the direct quantum approach and the full wave function of the 5D Universe is separated using a late-time approximation. Due to the compactness of the extra dimension, the momentum PS along the fifth dimension is quantized.