Non-minimally coupled scalar field cosmology on the phase plane

Abstract

In this publication we investigate dynamics of a flat FRW cosmological model with a non-minimally coupled scalar field with the coupling term $\xi R{\psi }^2$ in the scalar field action. The quadratic potential function $V(\psi )\propto {\psi }^2$ is assumed. All the evolutional paths are visualized and classified in the phase plane, at which the parameter of non-minimal coupling $\xi$ plays the role of a control parameter. The fragility of global dynamics with respect to changes of the coupling constant is studied in details. We find that the future big rip singularity appearing in the phantom scalar field cosmological models can be avoided due to non-minimal coupling constant effects. We have shown the existence of a finite scale factor singular point (future or past) where the Hubble function as well as its first cosmological time derivative diverges.

revtex4, 20 pages, 12 figs; (v2) title changed, analysis of critical points at infinity added, accepted to JCAP

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• Cosmological dynamics of dark energy in scalar-torsion $f(T,\varphi )$ gravity
• Effective gravitational coupling in modified teleparallel theories
• Starobinsky cosmological model in Palatini formalism
• Static spherically symmetric wormholes in generalized $f(R,\varphi )$ gravity
• A novel teleparallel dark energy model
• Constraints on dark energy from the lookback time versus redshift test
• Stability of scalar perturbations in scalar-torsion $f(T,\varphi )$ gravity theories in the presence of a matter fluid
• What $\xi$? Cosmological constraints on the non-minimal coupling constant
• Cosmological dynamics with non-minimally coupled scalar field and a constant potential function
• Observational Constraints on Dynamical Dark Energy Models
• Uniting cosmological epochs through the twister solution in cosmology with non-minimal coupling
• Spherical collapse in the extended quintessence cosmological models
• Do sewn singularities falsify the Palatini cosmology?
• Scalar-tensor cosmologies with dust matter in the general relativity limit
• Phase-space analysis of dark energy models in non-minimally coupled theories of gravity
• Twister quintessence scenario
• Dynamical description of a quintom cosmological model nonminimally coupled with gravity
• Polynomial $f(R)$ Palatini cosmology -- dynamical system approach
• Bifurcations in Ratra-Peebles quintessence models and their extensions
• The non-minimal coupling constant and the primordial de Sitter state
• Non-minimally Coupled Tachyon Field in Teleparallel Gravity
• Global Portraits of Nonminimal Inflation: Metric and Palatini
• Scalar Dark Energy Models and Scalar-Tensor Gravity: Theoretical Explanations for the Accelerated Expansion of Present Universe
• Cosmological Dynamics in Interacting Scalar-Torsion f(T,$\varphi$) Gravity: Investigating Energy and Momentum Couplings
• A new generic and structurally stable cosmological model without singularity
• From inflation to dark energy in scalar-tensor cosmology
• De Sitter ground state of scalar-tensor gravity and its primordial perturbation
• Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric
• Global portraits of nonminimal inflation
• Global Portraits of Inflation in Nonsingular Variables
• Interacting dark matter and q-deformed dark energy non-minimally coupled to gravity