Abstract
We study the autonomous system for a scalar–tensor model of dark energy with Gauss–Bonnet and non-minimal couplings. 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 are considered: power-law and exponential functions of the scalar field. For the exponential functions the existence of stable quintessence, phantom or de Sitter solutions, allows for an asymptotic behavior where the effective Newtonian coupling becomes constant. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation-dominated phases can also be described.
Highlights
The explanation of the late-time accelerated expansion of the universe, confirmed by different observations [1,2,3,4,5,6,7,8,9], represents one of the most important challenges of the modern cosmology
The Gauss Bonnet (GB) invariant coupled to a scalar field has been proposed to address the dark energy problem in [58], where it was found that quintessence or phantom phase may occur in the late-time universe
The scalar–tensor models represent a good source for modeling the dark energy and the explanation of the accelerated expansion of the universe
Summary
The explanation of the late-time accelerated expansion of the universe, confirmed by different observations [1,2,3,4,5,6,7,8,9], represents one of the most important challenges of the modern cosmology. According to the analysis of the observational data, the equation of state parameter w of the dark energy (DE) lies in a narrow region around the phantom divide (w = −1) and could even be below −1 All this motivates the study of alternative theoretical models that give a dynamical nature to DE, ranging from a variety of scalar fields of different nature [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] to modifications of general relativity that introduce large length scale corrections explaining the late-time behavior of the universe [28,29,30,31,32,33,34] (see [35,36,37,38] for review).
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