Extended Quintessence with non-minimally coupled phantom scalar field

TL;DR

This paper studies the late-time evolution of an extended quintessence model with a non-minimally coupled phantom scalar field, identifying conditions for different dynamical behaviors and the approach to the cosmological constant state.

Contribution

It introduces a dynamical systems analysis of extended quintessence with a non-minimally coupled phantom field, revealing conditions for oscillatory and monotonic approaches to the attractor.

Findings

Identification of two generic evolution scenarios: quasi-oscillatory and monotonic.

Derivation of conditions on the coupling constant for damping oscillations.

Explicit parametrization of the equation of state parameter w(z) for different scenarios.

Abstract

We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $\psi$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant. We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion that which cosmological scenario is realized depends on behavior of the system on the phase plane $(\psi, \psi')$. We formulate simple conditions on the value of coupling constant $\xi$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value $w=-1$. We describe this condition in terms of slow-roll parameters calculated at the critical point. We discover that the generic trajectories in the focus-attractor scenario come from the unstable node. It is also investigated the exact form of the parametrization of the equation of state parameter $w(z)$ (directly determined from dynamics) which assumes a different form for both scenarios.