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 wave function 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 wave function 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 for de Sitter.

27 pages, 8 figures

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• The Anthropic Landscape of String Theory
• Holographic probabilities in eternal inflation
• The Classical Universes of the No-Boundary Quantum State
• The No-Boundary Measure of the Universe
• The Multiverse Interpretation of Quantum Mechanics
• Hurdles for Recent Measures in Eternal Inflation
• A measure of the multiverse
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