Probabilities in the Bousso-Polchinski multiverse

Using the recently introduced method to calculate bubble abundances in an eternally inflating spacetime, we investigate the volume distribution for the cosmological constant $\Lambda$ in the context of the Bousso-Polchinski landscape model. We find that the resulting distribution has a staggered appearance which is in sharp contrast to the heuristically expected flat distribution. Previous successful predictions for the observed value of $\Lambda$ have hinged on the assumption of a flat volume distribution. To reconcile our staggered distribution with observations for $\Lambda$, the BP model would have to produce a huge number of vacua in the anthropic range $\Delta\Lambda_A$ of $\Lambda$, so that the distribution could conceivably become smooth after averaging over some suitable scale $\delta\Lambda\ll\Delta\Lambda_A$.