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

Area of Science:

• Cosmology
• Theoretical Physics
• Astrophysics

Background:

• Dark energy models are crucial for understanding cosmic acceleration.
• Scalar-tensor theories offer alternative frameworks to the standard cosmological model.
• Gauss-Bonnet and non-minimal couplings introduce complex dynamics in these theories.

Purpose of the Study:

• Investigate the autonomous system of a scalar-tensor dark energy model.
• Analyze critical points representing stable asymptotic cosmological scenarios.
• Examine the impact of power-law and exponential coupling functions on model behavior.

Main Methods:

• Analysis of the autonomous system for the scalar-tensor model.
• Identification and classification of critical points.
• Study of specific functional forms for coupling functions and scalar potential.

Main Results:

• Stable quintessence, phantom, and de Sitter attractor solutions were identified.
• Exponential coupling functions allow for constant effective Newtonian coupling in asymptotic regimes.
• Phantom solutions are possible without invoking ghost degrees of freedom.
• Transient inflationary and radiation-dominated phases can be described.

Conclusions:

• The studied scalar-tensor model provides a rich phenomenology for dark energy.
• Stable cosmic acceleration can be achieved through various mechanisms within this framework.
• The model offers a viable alternative for explaining cosmic acceleration without exotic physics.