Quantum Effects of an Extra Compact Dimension on the Wave Function of the Universe

We extended the direct quantum approach of the standard FRW cosmology from 4D to 5D and obtained a Hamiltonian formulation for a wave-like 5D FRW cosmology. Using a late-time approximation we isolated a y-part from the full wave function of the 5D Universe. Then we found that the compactness of the fifth dimension y yields a quantized spectrum for the momentum P₅ along the fifth dimension, and we have shown that the whole space-part of the wave function of the 5D Universe satisfies a 2D Schrödinger equation.