Probabilities in the Bousso-Polchinski multiverse

Abstract

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 $\delta \Lambda \ll \Delta {\Lambda }_A$.

21 pages, 7 figures Minor changes made

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