Why the cosmological constant is so small? A string theory perspective

With no free parameter (except the string scale MS), dynamical flux compactification in Type IIB string theory determines both the cosmological constant (vacuum energy density) Lambda and the Planck mass M-P in terms of M-S, thus yielding their relation. Following elementary probability theory, we find that a good fraction of the meta-stable de Sitter vacua in the cosmic string theory landscape tend to have an exponentially small cosmological constant Lambda compared to either the string scale M-S or the Planck scale M-P, i.e., Lambda << M-S(4) << M-P(4). Here we illustrate the basic stringy idea with a simple scalar field phi(3) (or phi(4)) model coupled with fluxes to show how this may happen and how the usual radiative instability problem is bypassed (since there are no parameters to be fine-tuned). These low lying semi-classical de Sitter vacua tend to be accompanied by light scalar bosons/axions, so the Higgs boson mass hierarchy problem may be ameliorated as well.