On Dynamics of Brans--Dicke Theory of Gravitation

Abstract

We study longstanding problem of cosmological clock in the context of Brans-Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogenous cosmological models. Then, we show that formulation of the Brans-Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann-Robertson-Walker cosmological models.

arXiv comment15 pages

References in corpus (26)

• Partial observables
• Quantum cosmological perfect fluid models
• Time-of-arrival in quantum mechanics
• Conditional probabilities with Dirac observables and the problem of time in quantum gravity
• Physical non-equivalence of the Jordan and Einstein frames
• Bouncing Universes with Varying Constants
• Some aspects of the cosmological conformal equivalence between ``Jordan Frame'' and ``Einstein Frame''
• GPS observables in general relativity
• General Relativity in terms of Dirac Eigenvalues
• Radiation-Dominated Quantum Friedmann Models
• Induced gravity inflation in the SU(5) GUT
• Dynamical Vacuum in Quantum Cosmology
• A Proposal for Solving the ``Problem of Time" in Canonical Quantum Gravity
• Self-Adjoint Wheeler-DeWitt Operators, the Problem of Time and the Wave Function of the Universe
• Applications of a New Proposal for Solving the "Problem of Time" to Some Simple Quantum Cosmological Models
• Solving the Problem of Time in General Relativity and Cosmology with Phantoms and k -- Essence
• The conformal status of $\omega =-3/2$ Brans-Dicke cosmology
• Cosmological Time in (2+1) - Gravity
• Time evolution of observable properties of parametrized systems
• Time evolution and observables in constrained systems
• The problem of time in parametrized theories
• The Problems of Time and Observables: Some Recent Mathematical Results
• Time and Observables in Unimodular General Relativity
• Eigenvalues of the Weyl operator as observables of general relativity
• Time and Dirac Observables in Friedmann Cosmologies
• On the Dynamics of Bianchi IX cosmological models

Cited by in corpus (14)

• Cosmological and Solar System Consequences of f(R,T) Gravity Models
• Cosmology of the selfaccelerating third order Galileon
• Cosmic acceleration in non-flat $f(T)$ cosmology
• Will there be again a transition from acceleration to deceleration in course of the dark energy evolution of the universe?
• Accelerating Bianchi Type-V Cosmology with Perfect Fluid and Heat Flow in Saez-Ballester Theory
• Scalar field quantum cosmology: a Schrödinger picture
• Chameleon Field Dynamics During Inflation
• Black holes in massive conformal gravity
• Black hole stability in Jordan and Einstein frames
• Noncommutative Universe and Chameleon Field Dynamics
• Cosmological Constant Implementing Mach Principle in General Relativity
• Quantum cosmology in an anisotropic n-dimensional universe
• Bouncing and inflationary dynamics in quantum cosmology in the de Broglie-Bohm interpretation
• Ether and Relativity