Linking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory

Based on the studies in Type IIB string theory phenomenology, we conjecture that a good fraction of the meta-stable de Sitter vacua in the cosmic stringy landscape tend to have a very small cosmological constant $\Lambda$ when compared to either the string scale $M_S$ or the Planck scale $M_P$, i.e., $\Lambda \ll M_S^4 \ll M_P^4$. These low lying de Sitter vacua tend to be accompanied by very light scalar bosons/axions. Here we illustrate this phenomenon with the bosonic mass spectra in a set of Type IIB string theory flux compactification models. We conjecture that small $\Lambda$ with light bosons is generic among de Sitter solutions in string theory; that is, the smallness of $\Lambda$ and the existence of very light bosons (may be even the Higgs boson) are results of the statistical preference for such vacua in the landscape. We also discuss a scalar field $\phi^3/\phi^4$ model to illustrate how this statistical preference for a small $\Lambda$ remains when quantum loop corrections are included, thus bypassing the radiative instability problem.