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

TL;DR

This paper uses dynamical systems methods to analyze the global behavior of a cosmological model with a non-minimally coupled scalar field and constant potential, revealing bifurcations and exact solutions.

Contribution

It provides a classification of all possible evolution paths and identifies bifurcation values of the coupling constant affecting the phase space structure.

Findings

Identified invariant manifold corresponding to accelerated expansion.

Derived an exact solution on the invariant manifold.

Discovered a special bifurcation value indicating potential symmetry.

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.