An 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. This has profound implications for applying the program of eternal inflation to making predictions in the string theory landscape.