The no-boundary measure in scalar–tensor gravity

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.

Fubini instantons in curved space

“…Then, we can paste the Lorentzian manifold t = 0 at the η = η 0 surface. This is possible only for the caseρ(η 0 ) =Φ(η 0 ) = 0, because of the Cauchy-Riemann theorem of complex analysis; otherwise, the Lorentzian manifold should be complex valued functions (for exceptional cases, we might be able to consider complex valued instantons, the so-called fuzzy instantons [55,56]). In this procedure, an event shows a spontaneous creation of the universe from 'nothing' [2], in which nothing means a state without the concept of classical spacetime [57].…”

Oscillating Instantons as Homogeneous Tunneling Channels

“…We use the steepest-descent method and consider only the on-shell solutions to count the probability from the path-integral [11,12,25,26]. We solve the classical equations of motion for Euclidean as well as Lorentzian time directionsφ…”

“…where I denotes the index of the canonical variables, then the wave function describes an almost classical behavior [11,12,25,26].…”

“…If we analytically continue all field values to be complexified functions, as in the case of the no-boundary measure [11,12,25,26], then we may obtain more instanton solutions. Before studying this process, in this paper, we will show that there are still quite a few real valued (not complex valued) instanton solutions with non-trivial field dynamics as homogeneous tunneling channels.…”

Euclidean quantum gravity and stochastic approach: Physical reality of complex-valued instantons

“…2. Hwang, Sahlmann and Yeom [4] and Hwang, Lee, Sahlmann and Yeom [5] discussed that complexvalued instantons are useful to explain the initial condition for the stabilization of dilaton or moduli fields. 3.…”