The no-boundary measure in scalar-tensor gravity

TL;DR

This paper investigates the no-boundary wave function in scalar-tensor gravity, revealing that quantum probabilities do not favor specific minima of potentials, challenging prior assumptions about the cosmological constant and dilaton stabilization.

Contribution

It provides a numerical analysis of the no-boundary measure in scalar-tensor gravity, showing that quantum effects do not prefer particular minima, contrasting with previous expectations.

Findings

No minima are substantially preferred by quantum probabilities.

Quantum effects lead to a non-preferential distribution over potential minima.

Results challenge the idea that zero cosmological constant is exponentially favored.

Abstract

In this article, we study the no-boundary wave function 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 done 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.