Quantum Cosmology in Bergmann-Wagoner Scalar-tensor Gravitational Theory

TL;DR

This paper solves the Wheeler-DeWitt equation within Bergmann-Wagoner scalar-tensor gravity for various cosmological functions, deriving quantum wormhole solutions and exploring classical and third quantization aspects of different universe models.

Contribution

It provides new exact solutions to the Wheeler-DeWitt equation for different scalar-tensor cosmologies, including quantum wormholes and third quantization analysis.

Findings

Quantum wormhole solutions for specific scalar-tensor functions

Exact solutions for Friedmann universes with different curvatures

Insights into classical and third quantization of minisuperspace models

Abstract

The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor gravitational theory in the case of Friedmann-Robertson- Walker cosmological model. We present solutions for several cosmological functions: i) \lambda(\phi)=0, ii) \lambda(\phi)=3\Lambda_0\phi and iii) a more complex \lambda(\phi), that depends on the choice of the coupling function, considering closed, flat and hyperbolic Friedmann universes (k=1, 0, -1). In the first two cases we show particular quantum wormhole solutions. Also, classical solutions are considered for some scalar-tensor theories, and we study the third quantization of some minisuperspace models.