On anthropic solutions of the cosmological constant problem

Motivated by recent work of Bousso and Polchinski (BP), we study theorieswhich explain the small value of the cosmological constant using the anthropicprinciple. We argue that simultaneous solution of the gauge hierarchy problemis a strong constraint on any such theory. We exhibit three classes of modelswhich satisfy these constraints. The first is a version of the BP model withprecisely two large dimensions. The second involves 6-branes and antibraneswrapped on supersymmetric 3-cycles of Calabi-Yau manifolds, and the third is aversion of the irrational axion model. All of them have possible problems inexplaining the size of microwave background fluctuations. We also find thatmost models of this type predict that all constants in the low energyLagrangian, as well as the gauge groups and representation content, are chosenfrom an ensemble and cannot be uniquely determined from the fundamental theory.In our opinion, this significantly reduces the appeal of this kind of solutionof the cosmological constant problem. On the other hand, we argue that thevacuum selection problem of string theory might plausibly have an anthropic,cosmological solution.Comment: JHEP LaTeX, 26 page