Preference for a Vanishingly Small Cosmological Constant in Supersymmetric Vacua in a Type IIB String Theory Model

TL;DR

This paper analyzes the probability distribution of the cosmological constant in a specific string theory model, showing a preference for a very small negative value and a high likelihood of stability as the number of moduli increases.

Contribution

It demonstrates that in a class of IIB string vacua, the probability distribution favors a vanishingly small cosmological constant and high stability with increasing moduli.

Findings

Probability distribution diverges at zero cosmological constant.

Median magnitude of  decreases exponentially with more moduli.

Probability of positive Hessian approaches unity as moduli increase.

Abstract

We study the probability distribution P(\Lambda) of the cosmological constant \Lambda in a specific set of KKLT type models of supersymmetric IIB vacua. We show that, as we sweep through the quantized flux values in this flux compactification, P(\Lambda) behaves divergent at \Lambda =0^- and the median magnitude of \Lambda drops exponentially as the number of complex structure moduli h^{2,1} increases. Also, owing to the hierarchical and approximate no-scale structure, the probability of having a positive Hessian (mass squared matrix) approaches unity as h^{2,1} increases.