A geometric-probabilistic method for counting low-lying states in the Bousso-Polchinski Landscape

TL;DR

The paper introduces a geometric-probabilistic approach to accurately count low-lying states with near-zero or positive cosmological constant in the Bousso-Polchinski Landscape, combining geometric lattice analysis and probabilistic modeling.

Contribution

It presents a novel method that combines geometric and probabilistic techniques to improve counting accuracy of states in the landscape.

Findings

The method provides accurate state counts near zero cosmological constant.

Numerical experiments support the validity of the probabilistic assumptions.

The approach enhances understanding of the distribution of cosmological constants.

Abstract

We propose an accurate method for counting states of close to zero and positive cosmological constant in the Bousso-Polchinski Landscape. This method is based on simple geometrical considerations on the high-dimensional lattice of quantized fluxes and on a probabilistic model (the "random hyperplane" model) that provides a distribution of the values of the cosmological constant. Justification of the assumptions made in this model are given by means of numerical experiments.