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.
Highlights
The detailed analysis of recent cosmological observations indicates that the universe has been through two accelerating phases [1,2,3,4]
We considered a cosmological model consisted by a Brans–Dicke field and a minimally coupled quintessence field in a spatially flat FLRW background space
The gravitational field equations consist of a Hamiltonian system of six degrees of freedom
Summary
The detailed analysis of recent cosmological observations indicates that the universe has been through two accelerating phases [1,2,3,4]. Action Integral is that of Brans–Dicke theory with an additional scalar field minimally coupled to gravity [43,44] This two-scalar-field model belongs to the family of multi-scalar field models which have been used as unified dark energy models [45,46,47] or as alternative models for the description of the acceleration phases of the universe [48,49,50,51]. The late-time acceleration phase, multifield cosmological models have been introduced to describe dark energy models with varying equation of state parameter which can cross the phantom divide line without the appearance of ghosts [54] Such models can be solved the Hubbletension problem [51].
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