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.

arXiv comment23 pages, 2 compound figures

References in corpus (35)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• In the Realm of the Hubble tension $-$ a Review of Solutions
• The galileon as a local modification of gravity
• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• The Hubble Space Telescope Cluster Supernova Survey: V. Improving the Dark Energy Constraints Above z>1 and Building an Early-Type-Hosted Supernova Sample
• Covariant Galileon
• Quintom Cosmology: Theoretical implications and observations
• A classification of scalar field potentials with cosmological scaling solutions
• Cosmological scaling solutions of non-minimally coupled scalar fields
• Perturbations in generalized multi-field inflation
• Generating the curvature perturbation at the end of inflation
• Dark energy from modified gravity with Lagrange multipliers
• The Dynamics of Multi-Scalar Field Cosmological Models and Assisted Inflation
• Hyperinflation
• Noether symmetry of F(T) cosmology with quintessence and phantom scalar fields
• Ghost-Free $F(R)$ Gravity with Lagrange Multiplier Constraint
• Dynamical symmetries in Brans-Dicke cosmology
• Dynamics of Chiral Cosmology
• Pure radiation in space-time models that admit integration of the eikonal equation by the separation of variables method
• Superpotential method for chiral cosmological models connected with modified gravity
• Expanding Spherically Symmetric Models without Shear
• Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory
• Crossing the phantom divide line as an effect of quantum transitions
• Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in the Stackel spaces of type (1.1)
• Primordial curvature perturbation during and at the end of multi-field inflation
• Cosmological Evolution of Two-Scalar fields Cosmology in the Jordan frame
• Exact Scalar-Tensor Cosmological Models
• Integrability from Point Symmetries in a family of Cosmological Horndeski Lagrangians
• Quadratic first integrals of autonomous conservative dynamical systems
• First integrals of holonomic systems without Noether symmetries
• Exact Solutions and Accelerating Universe in Modified Brans-Dicke Theories
• Lie and Noether point Symmetries for a Class of Nonautonomous Dynamical Systems
• Integrability of the mixmaster model
• The generic model of General Relativity
• Quadratic first integrals of time-dependent dynamical systems of the form ${\ddot{q}}^a=-{\Gamma }_{bc}^a{\dot{q}}^b{\dot{q}}^c-\omega (t)Q^a(q)$

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