Quantum Cosmology in Coupled Brans-Dicke Gravity: A Noether Symmetry Analysis

TL;DR

This paper explores a multi-field cosmological model in Brans-Dicke gravity using Noether symmetry to determine potentials and solutions, and extends to quantum cosmology via the Wheeler-DeWitt equation.

Contribution

It introduces a novel application of Noether symmetry to a coupled Brans-Dicke scalar field model, deriving classical and quantum solutions.

Findings

Determined scalar potential and coupling functions through symmetry analysis.

Obtained classical cosmological solutions with cyclic variables.

Formulated the Wheeler-DeWitt equation and identified conserved momenta.

Abstract

The present work deals with a multi-field cosmological model in a spatially flat FLRW space-time geometry. The usual Brans-Dicke(BD) field and another scalar field are minimally coupled to gravity while they interact with each other through the Kinetic terms. {The main aim of the present work is to examine whether the model is compatible with cosmic observations. So cosmological solutions are obtained using symmetry analysis only.} By imposing Noether Symmetry to the Lagrangian of the system the potential of the scalar field as well as the coupling function has been determined. The classical solutions are determined after simplifying the Lagrangian using cyclic variables. Finally, Wheeler-DeWitt(WD) equation in quantum cosmology has been formulated and conserved momenta corresponding to Noether symmetry shows the periodic part of the wave function and it helps to have the complete integral for the wave function.