Dynamical analysis for a scalar-tensor model with kinetic and non-minimal couplings

TL;DR

This paper analyzes a scalar-tensor dark energy model with non-minimal couplings, identifying stable solutions including quintessence, phantom, and de Sitter, with implications for gravitational interaction regimes and cosmic evolution.

Contribution

It introduces a detailed dynamical analysis of scalar-tensor models with specific non-minimal couplings, exploring stability and asymptotic behaviors for different functional forms.

Findings

Stable quintessence, phantom, and de Sitter solutions identified.

Asymptotic freedom regime for gravitational interaction in power-law couplings.

Phantom solutions without ghost degrees of freedom.

Abstract

We study the autonomous system for a scalar-tensor model of dark energy with non-minimal coupling to curvature and non-minimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential were considered: power-law and exponential functions of the scalar field. For power-law couplings, the restrictions on stable quintessence and phantom solutions lead to asymptotic freedom regime for the gravitational interaction. The model with dimensionless kinetic coupling constant gives stable de Sitter solutions. For the exponential functions the stable quintessence, phantom or de Sitter solutions, allow asymptotic behaviors where the effective Newtonian coupling can reach either the asymptotic freedom regime or constant value. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation dominated phases can also be described.