TL;DR
This paper investigates the quantum cosmology of brane worlds, demonstrating that inflating branes can originate from nothing and that extra dimensions influence quantum fluctuations during inflation.
Contribution
It provides a Hamiltonian analysis of brane world creation, showing the wave function matches 4D cosmology under specific conditions and discusses effects of bulk objects.
Findings
Inflating brane worlds can be created from nothing.
Wave functions in brane cosmology match 4D cases with Anti-de Sitter bulk.
Extra dimensions affect quantum fluctuations during inflation.
Abstract
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 Schrdinger 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.
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