Birth of the brane world

Birth of the brane world is studied using the Hamiltonian approach. It is shown that an inflating brane world can be created from nothing. The wave function of the universe obtained from the Wheeler de-Witt equation and the time-dependent Schrodinger equation for quantized scalar fields on the brane are the same as in the conventional 4-dimensional quantum cosmology if the bulk is exactly the Anti-de Sitter spacetime. The effect of the massive objects in the bulk is also discussed. This analysis tells us the presence of the extra dimension imprints a nontrivial effect on the quantum cosmology of the brane world. This fact is important for the analysis of the quantum fluctuations in the inflationary scenario of the brane world. (C) 2000 Elsevier Science B.V. All rights reserved.