Probabilities in the Bousso-Polchinski multiverse

TL;DR

This paper tests the conventional assumption of a flat volume distribution for the cosmological constant in the Bousso-Polchinski landscape by applying a gauge-invariant bubble-counting prescription. Using a perturbative treatment that treats upward transitions as small, the authors show that the resulting volume distribution is highly irregular and staggered, instead of flat, across the BP grid of vacua. They argue that reconciling this with the observed small value of Λ would require an immense number of anthropic vacua within the observational window to average out the fluctuations. The results have broad implications for predictions in landscape scenarios and suggest that flatness may not be a generic feature; additional work is needed to assess whether smoothing occurs in more realistic models or with different landscape statistics.

Abstract

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 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 $δΛ\llΔΛ_A$.

Figures (7)

• Figure 1: The factor $f(\Lambda/q_a^2,n_a)$ as a function of $\Lambda/q_a^2$ for $n_a=1$ (solid line), $n_a=2$ (dashed line), and $n_a=10$ (dotted line).
• Figure 2: The gravitational factor $r$ as a function of $\Lambda/|\Delta\Lambda_a|$ for $n_a=1$ (solid line), $n_a=2$ (dashed line), and $n_a=10$ (dotted line).
• Figure 3: The spectrum of vacua for a $J=7$, $N=4$ BP grid with parameters given in (\ref{['7D']}).
• Figure 4: The smoothed spectrum for the above model.
• Figure 5: Plot of $\log_{10}(1/p_j)$ vs. $\Lambda_j$ for the BP model with parameters given in (\ref{['7D']}). The star marks the dominant vacuum $\alpha_*$. Triangles represent vacua in group 1, squares in group 2, diamonds in groups 3 and 6, crosses in groups 4 and 7, and points in groups 5 and 8.