New conservation laws and exact cosmological solutions in Brans-Dicke cosmology with an extra scalar field

TL;DR

This paper introduces a novel method for deriving conservation laws in a two-field Brans-Dicke cosmological model, leading to new exact solutions and stability analysis of scaling solutions.

Contribution

It presents a new technique for deriving conservation laws without variational symmetries in a two-field Brans-Dicke model with a quintessence field.

Findings

New conservation laws derived for the model

Exact cosmological solutions obtained

Stability criteria for scaling solutions established

Abstract

The derivation of conservation laws and invariant functions is an essential procedure for the investigation of nonlinear dynamical systems. In this study we consider a two-field cosmological model with scalar fields defined in the Jordan frame. In particular we consider a Brans-Dicke scalar field theory and for the second scalar field we consider a quintessence scalar field minimally coupled to gravity. For this cosmological model we apply for the first time a new technique for the derivation of conservation laws without the application of variational symmetries. The results are applied for the derivation of new exact solutions. The stability properties of the scaling solutions are investigated and criteria for the nature of the second field according to the stability of these solutions are determined.