Why the Cosmological Constant is so Small ? A String Theory Perspective

With no free parameter (except the string scale $M_S$), 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., $\Lambda \ll M_S^4 \ll M_P^4$. Here we illustrate the basic stringy ideas 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.