Probabilities in the Arkani-Hamed-Dimopolous-Kachru landscape

TL;DR

This paper investigates the probability distribution of the cosmological constant in string theory landscapes, specifically analyzing the Arkani-Hamed-Dimopolous-Kachru model to understand the variability and structure of these distributions.

Contribution

It demonstrates that the staggered distribution of the cosmological constant observed in Bousso-Polchinski models also appears in the simpler Arkani-Hamed-Dimopolous-Kachru landscape, supporting a broader conjecture.

Findings

The volume distribution for the cosmological constant is staggered.

The distribution varies wildly in the landscape models.

The conjecture about the universality of the staggered distribution is supported.

Abstract

In a previous paper we found that in the context of the string theory ``discretuum'' proposed by Bousso and Polchinski, the cosmological constant probability distribution varies wildly. However, the successful anthropic predictions of the cosmological constant depend crucially on the assumption of a flat prior distribution. We conjectured that the staggered character of our Bousso-Polchinski distribution will arise in any landscape model which generates a dense spectrum of low-energy constants from a wide distribution of states in the parameter space of the fundamental theory. Here we calculate the volume distribution for $\Lambda$ in the simpler Arkani-Hamed-Dimopolous-Kachru landscape model, and indeed this conjecture is borne out.