Quantum and classical cosmology in the Brans-Dicke theory

TL;DR

This paper explores classical and quantum cosmological models in Brans-Dicke theory, analyzing bounce solutions, quantization, and the effects of energy conditions and the parameter  on singularities and quantum behavior.

Contribution

It provides a comprehensive analysis of both classical and quantum cosmology in Brans-Dicke theory, including bounce solutions and the application of Bohmian mechanics for  > -3/2.

Findings

Bounce solutions obeying energy conditions are identified.

Quantum solutions show singularity avoidance for  < -3/2.

Bohmian mechanics allows analysis of quantum effects for  > -3/2.

Abstract

In this paper we discuss classical and quantum aspects of cosmological models in Brans-Dicke theory. First, we review cosmological bounce solution in Brans-Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then we quantize this classical model in a canonical way, establishing the corresponding Wheeler-DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case $\omega<-3/2$, the energy is bounded from below and singularity-free solutions are found. However, in the case $\omega> -3/2$ we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). But we can analyze this case using Bohmian mechanics and the de Broglie-Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of $\omega$.