The creation of an inflating brane-world can be modelled as a de
Sitter instanton in a way that closely follows the 4D instanton, as
shown in [104]. The instanton
consists of two identical patches of joined together
along a de Sitter brane () with compact spatial
sections. The instanton describes the “birth” of both the inflating
brane and the bulk spacetime, which are together “created from
nothing”, i.e., the point at the south pole of the de Sitter
4-sphere. The Euclidean metric is
where is a 3-sphere, and . The Euclidean instanton interpolates between (“nothing”) and (the created
universe), which is a spherical brane of radius
After creation, the brane-world evolves according to the Lorentzian
continuation, ,