Noether Symmetry Analysis for Generalized Brans-Dicke Cosmology

TL;DR

This paper performs a symmetry analysis of generalized Brans-Dicke cosmology with an additional scalar field, identifying integrable models and classifying variational symmetries to facilitate exact solutions.

Contribution

It provides a complete classification of variational symmetries and introduces new integrable cosmological models within generalized Brans-Dicke theory.

Findings

Identified functional forms leading to integrability.

Presented new families of integrable cosmological models.

Enhanced understanding of symmetry structures in scalar-tensor theories.

Abstract

We present the complete solution to the classification problem regarding the variational symmetries of the generalized Brans-Dicke cosmological model in the presence of a second scalar field minimally coupled to gravity and the generalized Brans-Dicke scalar field theory. Through the symmetry analysis, we were able to specify the functional form of the field equations such that they become integrable. Additionally, new families of integrable cosmological models are presented.