Non-minimally coupled scalar field dark sector of the universe: in-depth (Einstein frame) case study

TL;DR

This paper investigates non-minimally coupled scalar-tensor cosmological models in the Einstein frame, analyzing their dynamics and stability to understand evolving dark energy and dark matter interactions in the universe.

Contribution

It provides a comprehensive dynamical systems analysis of five scalar field models with non-minimal coupling, including stability and physical interpretation, based on recent observational data.

Findings

Critical points identified with stability analysis

Energy transfer mechanisms between scalar field and matter elucidated

Models consistent with observational constraints analyzed

Abstract

In this study, motivated by recent results from DESI DR2 suggesting the existence of evolving/interacting dark energy, we analyze spatially flat FLRW interacting scalar-tensor cosmological models with non-minimal coupling (NMC) between the scalar field (SF) and matter/cosmological dust in the Einstein conformal frame. By using modified expansion normalized variables that account for negative values of the scalar field potential, we derive cosmological dynamical system equations and expressions for physical variables. Five specific scalar field models (axions/ALPs, cyclic ekpyrotic, exponential with a constant, quintessence, and SFDM) are examined in depth to determine how they evolve, as they are thought to represent evolving dark energy in the late Universe. Using appropriate mathematical methods (e.g. linear stability, center manifold and Poincar\'e sphere), we present critical points along with their character and physical interpretation with respect to the possible evolution of the Universe. Considering both positive and negative values of the coupling parameter allows us to examine the transfer of energy from the scalar sector to dust and from matter to the scalar field. Considering four different values of this parameter provides a comprehensive analysis that incorporates all significant types of dynamical system evolution (from mathematical and physical perspectives). The initial conditions for the in-depth numerical analysis were calculated analytically from Planck 2018 and DESI DR2 CPL parametrizations.