Cosmological dynamics with non-minimally coupled scalar field and a constant potential function

Abstract

Dynamical systems methods are used to investigate global behavior of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We show that the system can be reduced to an autonomous three-dimensional dynamical system and additionally is equipped with an invariant manifold corresponding to an accelerated expansion of the universe. Using this invariant manifold we find an exact solution of the reduced dynamics. We investigate all solutions for all admissible initial conditions using theory of dynamical systems to obtain a classification of all evolutional paths. The right-hand sides of the dynamical system depend crucially on the value of the non-minimal coupling constant therefore we study bifurcation values of this parameter under which the structure of the phase space changes qualitatively. We found a special bifurcation value of the non-minimal coupling constant which is distinguished by dynamics of the model and may suggest some additional symmetry in matter sector of the theory.

39 pages, 8 multiple figs; v2. 41 pages, 8 multiple figs. published version

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• Classes of non-minimally coupled scalar fields in spatially curved FRW spacetimes
• Dynamical description of a quintom cosmological model nonminimally coupled with gravity
• The non-minimal coupling constant and the primordial de Sitter state
• Induced Gravity and Quantum Cosmology
• Cosmological dynamics and bifurcation analysis of the general non-minimally coupled scalar field models
• Non-Minimal Inflation with a scalar-curvature mixing term $\frac{1}{2}\xi R{\varphi }^2$
• A new generic and structurally stable cosmological model without singularity
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• The cosmological constant and a scalar field coupled non minimally to gravity
• Global portraits of nonminimal inflation
• Global Portraits of Inflation in Nonsingular Variables
• Can an Extra Degree of Freedom in Scalar-Tensor Non-Metricity Gravity Account for the Evolution of the Universe?
• Dynamical analysis of Brans-Dicke Universe with inverse power-law effective potential
• Energy momentum tensor of a non-minimally coupled scalar from the equivalence of the Einstein and Jordan frames