Bubbles in the Self-Accelerating Universe

TL;DR

This paper investigates the stability of the self-accelerating universe in the Dvali-Gabadadze-Porrati model, concluding that certain bubble nucleation processes are unphysical unless negative tension walls are considered, implying the branch's stability.

Contribution

It demonstrates that thin wall instantons for bubble nucleation in this model are unphysical, challenging previous assumptions about branch decay and stability.

Findings

Thin wall instantons cannot be realized as smooth solutions.

No O(4) symmetric solutions connect the branches without negative tension.

Self-accelerating branch is stable against bubble nucleation in standard conditions.

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.