We discuss the brane world model of Dvali, Gabadadze and Porrati in which
branes evolve in an infinite bulk and the brane curvature term is added to the
action. If Z_2 symmetry between the two sides of the brane is not imposed, we
show that the model admits the existence of "stealth branes" which follow the
standard 4D internal evolution and have no gravitational effect on the bulk
space. Stealth branes can nucleate spontaneosly in a Minkowski bulk. This
process is described by the standard 4D quantum cosmology formalism with
tunneling boundary conditions for the brane world wave function. The notorious
ambiguity in the choice of boundary conditions is fixed in this case due to the
presence of the embedding spacetime. We also point to some problematic aspects
of models admitting stealth brane solutions.Comment: 24 pages; Final version, to appear in Phys. Rev. D. The discussion of
"embeddability obstruction" is removed (thanks to Takahiro Tanaka who
convinced us that there is no such obstruction
