Quantum Cosmology of the Brane Universe

We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild–anti-de Sitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the problem of initial conditions, is conceptually more simple than in the $(3+1)$-dimensional case. The Wheeler-DeWitt equation is a finite-difference equation. It is exactly solvable in the case of a flat universe and we find the ground state of the system. The closed brane universe can be created as a result of decay of the bulk black hole.

Figure 1

The potential $U$ (9) for different choices of parameters. The potential is singular at the gravitational radius of the bulk Schwarzschild–anti-de Sitter black hole when $M\ne 0$.