Bubbles in the self-accelerating universe

Abstract

We revisit the issue of the stability in the Dvali-Gabadadze-Porrati model by considering the nucleation of bubbles of the conventional branch within the self-accelerating branch. We construct an instanton describing this process in the thin wall approximation. On one side of the bubble wall, the bulk consists of the exterior of the brane, while on the other side it is the interior. The solution requires the presence of a 2-brane (the bubble wall) which induces the transition. However, we show that this instanton cannot be realized as the thin wall limit of any smooth solution. Once the bubble thickness is resolved, the equations of motion do not allow $O(4)$ symmetric solutions joining the two branches. We conclude that the thin wall instanton is unphysical, and that one cannot have processes connecting the two branches, unless negative tension bubble walls are introduced. This also suggests that the self-accelerating branch does not decay into the conventional branch nucleating bubbles. We comment on other kinds of bubbles that could interpolate between the two branches.