Quantum and classical cosmology in the Brans-Dicke theory

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 $\omega$.

arXiv commentPublished in the Special Issue "Quantum cosmology", Universe 7(8), 286; guest editor Paulo Moniz

References in corpus (20)

• The Confrontation between General Relativity and Experiment
• The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang
• Superstring Cosmology
• A Critical Review of Classical Bouncing Cosmologies
• Quantum cosmology from the de Broglie-Bohm perspective
• Solving the measurement problem: de Broglie-Bohm loses out to Everett
• Illusions of general relativity in Brans-Dicke gravity
• Bouncing Cosmology made simple
• Gaussian superpositions in scalar-tensor quantum cosmological models
• Singularities and Classical Limit in Quantum Cosmology
• The Bohm Interpretation of Quantum Cosmology
• Has the Universe always expanded ?
• Scalar-tensor gravity and conformal continuations
• What's wrong with Einstein's 1927 hidden-variable interpretation of quantum mechanics?
• Quantum cosmology with scalar fields: self-adjointness and cosmological scenarios
• Stiff Matter Solution in Brans-Dicke Theory and The General Relativity Limit
• Regular Bouncing Solutions, Energy Conditions and the Brans-Dicke Theory
• Cosmological models with asymmetric quantum bounces
• From pre- to post-big bang: an (almost) self-dual cosmological history
• Quantum cosmology of scalar-tensor theories and self-adjointness

Cited by in corpus (3)

• Analytic Solutions of Brans-Dicke Cosmology: Early Inflation and Late Time Accelerated Expansion
• Gravitational Collapse without Singularity Formation in Brans-Dicke Theory
• The Unruh effect under the de Broglie-Bohm perspective