FRW in cosmological self-creation theory: Hamiltonian approach

TL;DR

This paper explores the Hamiltonian approach to Friedmann-Robertson-Walker cosmology within self-creation theory, deriving classical and quantum solutions using Hamilton-Jacobi and Lagrange-Charpit methods for various barotropic parameters.

Contribution

It introduces a Hamiltonian framework for FRW cosmology in self-creation theory and provides classical and quantum solutions for different barotropic parameters.

Findings

Classical solutions obtained for all barotropic parameters.

Quantum solutions derived through characteristic surfaces.

Framework extends previous models with new Hamiltonian and quantum analysis.

Abstract

We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition $\rm[\frac{1}{\phi}(8\pi T^{\mu \nu (M)}+T^{\mu\nu (\phi)})]_{;\nu}=0$. We take as a first model the flat FRW metric in the Hamilton-Jacobi scheme and we present the Lagrange-Charpit approach in order to find classical solutions. In the quantum scheme, once we determine the characteristic surfaces, the quantum solution is obtained. These two classes of solutions are found for all values of the barotropic parameter $\gamma$.