That emptiness, Carroll suggests, would be a high-entropy environment technically known as de Sitter space.
Although the baby would have low entropy, the total entropy of the system (mother de Sitter space plus baby) would be higher, preserving the second law.
Best of all, that scenario can happen in both directions of time, because de Sitter space can spawn many spacetime bubbles.
Furthermore, Zheng  studied spacelike hypersurfaces in the de Sitter space
An example of the Casimir effect in curved spacetime has been considered for spherical geometries  in de Sitter space  and in the background of static domain wall .
Casimir effect for a spherical shell in de Sitter space.
4] of 4 complex dimensions is an 8 real-dim Hyperboloid of constant negative scalar curvature that can be identified with the conformal relativistic curved phase space associated with the electron (a particle) moving in a 4D Anti de Sitter space Ad[S.
mu]], up to a crucial scale factor R, given by the size of the Anti de Sitter space (de Sitter space) throat.
10] associated with a particle moving in the 5D Anti de Sitter space Ad[S.
10] corresponding to the conformal relativistic curved phase space of a particle moving in 5D Anti de Sitter Space Ad[S.