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 Λ in the context of the Bousso Polchinski (BP) 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 Λ have hinged on the assumption of a flat volume distribution. To reconcile our staggered distribution with observations for Λ, the BP model would have to produce a huge number of vacua in the anthropic range ΔΛ_A of Λ, so that the distribution could conceivably become smooth after averaging over some suitable scale \delta \Lambda \ll \Delta \Lambda_A .