Conservation laws and Exact Solutions in Brans-Dicke Cosmology with a Scalar Field

Abstract

Scalar-tensor theories have drawn the attention of cosmologist for the past few years because they can provide mechanism to explain the observable phenomena. Moreover, the results of scalar-tensor theories can be applied in higher-order theories of gravity. In this work, we consider a Brans-Dicke scalar field cosmological model that includes a second scalar field minimally coupled to gravity. For the second scalar field we consider the two cases that there exist and there is not any interaction with the Brans-Dicke scalar field. For the two models of our consideration we prove the existence of scaling and de Sitter solutions. Furthermore, we perform an Obsiannikov's classification for the field equations, where we find all the point and contact transformations which leave the gravitational Action Integral invariant. Conservation laws are determined and we show how these can be applied to infer about the integrability of the cosmological models and find new analytic solutions.

arXiv comment14 pages, no figures, version to appear in General Relativity and Gravitation

References in corpus (47)

• The Cosmological Constant and Dark Energy
• Modified Gravity and Cosmology
• The galileon as a local modification of gravity
• Covariant Galileon
• Quintom Cosmology: Theoretical implications and observations
• Cosmological Evolution of a Quintom Model of Dark Energy
• Quintessence: A Review
• Are f(R) dark energy models cosmologically viable ?
• Higher order gravity theories and scalar tensor theories
• Cosmological Solutions of $f(T)$ Gravity
• Using the Noether symmetry approach to probe the nature of dark energy
• Illusions of general relativity in Brans-Dicke gravity
• Hyperinflation
• Quintom Cosmology with General Potentials
• Selected topics in scalar-tensor theories and beyond
• Noether symmetries in Bianchi universes
• Two scalar field cosmology: Conservation laws and exact solutions
• The past and future dynamics of quintom dark energy models
• Noether Symmetries as a geometric criterion to select theories of gravity
• Gravity and Scalar Fields
• Attractor Behaviour in Multifield Inflation
• Ghost-Free $F(R)$ Gravity with Lagrange Multiplier Constraint
• $f(R)$-gravity from Killing Tensors
• Teleparallel dark energy model with a fermionic field via Noether symmetry
• Classification of the Horndeski cosmologies via Noether Symmetries
• Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory
• The General Solution of Bianchi Type III Vacuum Cosmology
• Global integrability of cosmological scalar fields
• Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities
• Noether analysis of Scalar-Tensor Cosmology
• Dynamical symmetries in Brans-Dicke cosmology
• Gravitational scalar-tensor theory
• Counting Components in the Lagrange Multiplier Formulation of Teleparallel Theories
• Cosmological Solutions in Multiscalar Field Theory
• Automorphisms and a Cartography of the Solution Space for Vacuum Bianchi Cosmologies: The Type III Case
• Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory
• Evolution of Dynamical Coupling in Scalar Tensor Theory from Noether Symmetry
• The General Solution of Bianchi Type $VI{I}_h$ Vacuum Cosmology
• Noether symmetry in $f(T)$ teleparallel gravity
• Integrability from Point Symmetries in a family of Cosmological Horndeski Lagrangians
• Exact Scalar-Tensor Cosmological Solutions via Noether Symmetry
• Exact Cosmological Solutions of $f(R)$ Theories via Hojman Symmetry
• Hamiltonian Analysis of Lagrange Multiplier Modified Gravity
• On the Hojman conservation quantities in Cosmology
• Duality transformation and conformal equivalent scalar-tensor theories
• Discrete spectrum of the quantum Reissner - Nordström geometry
• Integrability of the mixmaster model

Cited by in corpus (10)

• In the Realm of the Hubble tension $-$ a Review of Solutions
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Emergent Dark Energy, neutrinos and cosmological tensions
• Dark matter signatures of black holes with Yukawa potential
• Cosmological Evolution of Two-Scalar fields Cosmology in the Jordan frame
• Charged Black Holes with Yukawa Potential
• Stability of a modified Jordan-Brans-Dicke theory in the dilatonic frame
• Dynamical description of a quintom cosmological model nonminimally coupled with gravity
• Quadratic integrals of a multi-scalar cosmological model
• Classical and Quantum cosmology for two scalar field Brans-Dicke type theory: A Noether Symmetry approach