The no-boundary measure in scalar-tensor gravity

Abstract

In this paper, we study the no-boundary wavefunction in scalar-tensor gravity with various potentials for the non-minimally coupled scalar field. Our goal is to calculate probabilities for the scalar field-and hence the effective gravitational coupling and cosmological constant-to take specific values. Most calculations are performed in the minisuperspace approximation, and we use a saddle point approximation for the Euclidean action, which is then evaluated numerically. We find that for potentials that have several minima, none of them is substantially preferred by the quantum-mechanical probabilities. We argue that the same is true for the stable and the runaway solution in the case of a dilaton-type potential. Technically, this is due to the inclusion of quantum-mechanical effects (fuzzy instantons). These results are in contrast to the often-held view that vanishing gravitation or cosmological constants would be exponentially preferred in quantum cosmology, and they may be relevant to the cosmological constant problem and the dilaton stabilization problem.