Brane-world instanton

5.2 Brane-world instanton

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 [105

]. The instanton consists of two identical patches of $AdS5$ joined together along a de Sitter brane ( $dS4$ ) 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 $AdS5$ metric is

where $dΩ2(3)$ is a 3-sphere, and $r ≤ r0$ . The Euclidean instanton interpolates between $r = 0$ (“nothing”) and $r = r0$ (the created universe), which is a spherical brane of radius

After creation, the brane-world evolves according to the Lorentzian continuation, $χ → iH0t + π ∕2$ ,

(see Figure 7

Figure 7:

Brane-world instanton. (Figure taken from [105

].)