Obstacle to populating the string theory landscape

We construct domain walls and instantons in a class of models with coupled scalar fields, determining, in agreement with previous studies, that many such solutions contain naked timelike singularities. Vacuum bubble solutions of this type do not contain a region of true vacuum, obstructing the ability of eternal inflation to populate other vacua. We determine a criterion that potentials must satisfy to avoid the existence of such singularities and show that many domain wall solutions in type IIB string theory are singular.

Figure 1

A Euclidean potential that leads to singular domain wall and instanton solutions. The arrow indicates the strong gradient towards $-\chi$ that exists away from vacuum.

Figure 2

The time-symmetric thin-wall singular vacuum bubble spacetime. The shaded region is described by the solution to Eq. (4). The bubble wall is the thick solid line at ${\xi }_w$, and the singularity is the dashed line (beyond which the nonsingular solution would have relaxed to the true vacuum).