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

TL;DR

This paper explores the no-boundary wave function in string theory, demonstrating its role in moduli stabilization, flux compactification, and predicting the likelihood of different cosmological constants, favoring negative values.

Contribution

It provides new insights into how the no-boundary measure influences moduli stabilization and the probability distribution of the cosmological constant in string theory models.

Findings

No classical histories exist for exponential potentials beyond a critical slope.

The no-boundary wave function stabilizes moduli in the flux compactification model.

Negative cosmological constants are statistically favored over zero or positive values.

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.