On anthropic solutions of the cosmological constant problem

Motivated by recent work of Bousso and Polchinski (BP), we study theories w hich explain the small value of the cosmological constant using the anthrop ic principle. We argue that simultaneous solution of the gauge hierarchy pr oblem is a strong constraint on any such theory. We exhibit three classes o f models which satisfy these constraints. The first is a version of the BP model with precisely two large dimensions. The second involves 6-branes and antibranes wrapped on supersymmetric 3-cycles of Calabi-Yau manifolds, and the third is a version of the irrational axion model. All of them have pos sible problems in explaining the size of microwave background fluctuations. We also find that most models of this type predict that all constants in t he low energy lagrangian, as well as the gauge groups and representation co ntent, are chosen from an ensemble and cannot be uniquely determined from t he fundamental theory. In our opinion, this significantly reduces the appea l of this kind of solution of the cosmological constant problem. On the oth er hand, we argue that the vacuum selection problem of string theory might plausibly have an anthropic, cosmological solution.