Dynamical interplay between coupled scalar dark sectors and gravity

TL;DR

This work develops a cosmological model with two scalar dark-sector fields $φ$ and $χ$ non-minimally coupled to gravity through the scalar curvature, extending an axion–dilaton system. By adopting exponential potentials and curvature couplings and recasting the system as an autonomous dynamical system, the authors reveal a diverse set of fixed points with distinct $w_{\rm eff}$ and stability properties. Several fixed points provide saddle trajectories and scaling solutions, including a zero-EOS scaling branch that can alleviate the cosmic coincidence problem while allowing acceleration. The results offer a framework for extending to additional geometric invariants and for future observational tests.

Abstract

We explore a novel cosmological model based on coupled fields in the framework of scalar tensor theories, considering the specific interplay between gravity and scalar fields. The model further extends a recent axion-dilaton system by introducing viable couplings with the space--time geometry encoded into the scalar curvature. After briefly introducing the action and the corresponding field equations, we employ linear stability theory to investigate the physical properties. The analysis showed the compatibility of the current theoretical model with the recent history of the Universe, obtaining viable constraints for the model's parameters in some specific cases. In the present setup, the axion--dilaton system is non--minimally coupled with gravity in an independent manner, leading to distinct physical features in the phase-space structure, possible alleviating the cosmic coincidence problem.

Figures (12)

• Figure 1: The figure describes a possible saddle region for the $P_1$ critical line.
• Figure 2: The effective equation of state for the $P_1$ solution.
• Figure 3: The effective equation of state for the $P_2$ solution.
• Figure 4: The effective equation of state for the $P_4^{+}$ solution ($\beta=1, \lambda_1=1, \alpha_1=1$).
• Figure 5: The contour for the $P_4^{+}$ solution where $w_{eff}=0$ ($\alpha_1=1, \lambda_1=1$).