On Dynamics of Brans--Dicke Theory of Gravitation

TL;DR

This paper explores the dynamics of Brans-Dicke gravity, presenting a Hamiltonian formulation and identifying a cosmological time variable in quantum cosmology, with applications to FRW models.

Contribution

It introduces a Hamiltonian framework for Brans-Dicke theory and demonstrates how to define a cosmological time variable in quantum cosmology.

Findings

Hamiltonian formulation for spatially homogeneous models

Identification of a scalar-field-based cosmological time

Application to classical and quantum FRW models

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.