The no-boundary measure in string theory: applications to moduli stabilization, flux compactification and cosmic landscape

Abstract

We investigate the no-boundary measure in the context of moduli stabilization. To this end, we first show that for exponential potentials, there are no classical histories once the slope exceeds a critical value. We also investigate the probability distributions given by the no-boundary wavefunction near maxima of the potential. These results are then applied to a simple model that compactifies 6D to 4D (HBSV model) with fluxes. We find that the no-boundary wavefunction effectively stabilizes the moduli of the model. Moreover, we find the a priori probability for the cosmological constant in this model. We find that a negative value is preferred, and a vanishing cosmological constant is not distinguished by the probability measure. We also discuss the application to the cosmic landscape. Our preliminary arguments indicate that the probability of obtaining anti-de Sitter space is vastly greater than that for de Sitter.