We study the possible types of the nucleation of vacuum bubbles. We classify vacuum bubbles in de Sitter background and present some numerical solutions. The thin-wall approximation is employed to obtain the nucleation rate and the radius of vacuum b
ubbles. With careful analysis we confirm that Parkes formula is also applicable to the large true vacuum bubbles. The nucleation of the false vacuum bubble in de Sitter background is also evaluated. The tunneling process in the potential with degenerate vacua is analyzed as the limiting cases of the large true vacuum bubble and false vacuum bubble. Next, we consider the pair creation of black holes in the background of bubble solutions. We obtain static bubble wall solutions of junction equation with black hole pair. The masses of created black holes are uniquely determined by the cosmological constant and surface tension on the wall. Finally, we obtain the rate of pair creation of black holes.
We study the dynamics of false vacuum bubbles. A nonminimally coupled scalar field gives rise to the effect of negative tension. The mass of a false vacuum bubble from outside observers point of view can be positive, zero, or negative. The interior f
alse vacuum has de Sitter geometry, while the exterior true vacuum background can have geometry depending on the vacuum energy. We show that there exist expanding false vacuum bubbles without the initial singularity in the past.
