Bubbles in the Self-Accelerating Universe

TL;DR

The paper investigates the nonperturbative stability of the self-accelerating (SA) branch in the DGP brane-world by analyzing the nucleation of bubbles of the conventional branch via a Euclidean instanton in the thin-wall limit. It derives a wall-tension dependent matching condition on the bubble and shows that a branch-changing instanton can exist only with a wall tension, but cannot be realized as a smooth, scalar-field-based solution; consequently, no $O(4)$-symmetric decay from SA to the conventional branch is supported. The authors argue that the thin-wall instanton is unphysical in the full dynamics, implying that SA does not decay by such bubble nucleation, though other non-bubble channels or ghost-related effects may be relevant. The work clarifies stability aspects of the SA branch and discusses related strong-coupling concerns and alternative bubble configurations within the DGP framework.

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.

Figures (5)

• Figure 1: Trajectory of the brane in $(z,r)$ plane (for $\sigma>0$).
• Figure 2: Relation between $\rho_E$ and $\hat{K}$. we do not have to consider dashed line. Any solution that smoothly joins the two branches must have an energy density $\rho_E=-\rho_c$ at some point.
• Figure 3: In the upper panel we sketch the form of $\rho_E(\tau)$ for a solution that smoothly joins the two branches. At the point $B$, we have $\rho=-\rho_c$. In the lower panel, we show schematically the trajectory starting from the conventional branch. At point $A$, $\rho_E$ vanishes, and so does the extrinsic curvature. The bulk is the interior ($r<r(\tau)$) before that point and the exterior ($r>r(\tau)$) after it. At point $B$, by the conservation equation, $r(\tau)$ develops a minimum at $2r_c$. However, matching to the SA branch at point $B$ is incompatible with Eq. (\ref{['r']}).
• Figure 4: Null bubble in the full DGP model. The two branches are connected on a light cone. The upper half of this geometry is given by the continuation of the instanton in Fig. 1 in the limit when the bubble wall tension vanishes. The lower half is the 'background' solution, given by the SA branch. In the $\pi$ language, it corresponds to the solution \ref{['null']}.
• Figure 5: Inverse null bubble in the DGP model. In this configuration, the brane is in the SA branch in the interior of the future light cone of some event.