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

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.

23 pages, 2 compound figures

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Cited by in corpus (8)

• Algebra of the symmetry operators of the Klein-Gordon-Fock equation for the case when groups of motions $G_3$ act transitively on null subsurfaces of spacetime
• Maxwell's equations in homogeneous spaces for admissible electromagnetic fields
• Algebras of integrals of motion for the Hamilton-Jacobi and Klein-Gordon-Fock equations in spacetime with a four-parameter groups of motions in the presence of an external electromagnetic field
• Maxwell equations in homogeneous spaces with solvable groups of motions
• Integrable modified gravity cosmological models with an additional scalar field
• Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions
• Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions
• Integrable Cosmological Models with an Arbitrary Number of Scalar Fields