WKB Wave Functions with the Induced Gravity Theory

TL;DR

This paper constructs and solves the Wheeler-DeWitt equation for induced gravity using WKB approximation under various boundary conditions, revealing that quantum creation leads to constant gravitational and cosmological constants, with implications for the tunneling wave function.

Contribution

It introduces a quantum cosmological analysis of induced gravity with boundary conditions, showing constants emerge from quantum creation and analyzing wave function behaviors.

Findings

Constants become fixed after quantum creation regardless of classical variations.

Tunneling wave function peaks when the cosmological constant is zero.

Different boundary conditions influence the form of the wave function.

Abstract

The Wheeler-DeWitt equation for the induced gravity theory is constructed in the minisuperspace approximation, and then solved using the WKB method under three types of boundary condition proposed respectively by Hartle & Hawking (``no boundary''), Linde and Vilenkin (``tunneling from nothing''). It is found that no matter how the gravitational and cosmological ``constants'' vary in the classical models, they will acquire constant values when the universe comes from quantum creation, and that, in particular, the resulting tunneling wave function under the Linde or Vilenkin boundary condition reaches its maximum value if the cosmological constant vanishes.