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

TL;DR

The paper analyzes spatially flat FLRW cosmologies with non-minimal coupling in the Einstein frame by formulating a closed 4D autonomous system using variables (x,u,Ω_r,λ_φ). It studies five well-motivated scalar-field potentials (axions/ALPs, cyclic ekpyrotic, exponential with a plateau, tracking quintessence, and SFDM) to map their fixed points, stability, and possible cosmic histories, including both expanding and contracting branches. Through linear stability, center-manifold, and Poincaré analyses, it identifies how energy transfer between the scalar sector and dust (via Q = β φ˙ ρ_m) shapes evolution, including regimes with negative potentials that can drive turnaround or ekpyrotic contraction. Numerical explorations anchored to Planck 2018 and DESI DR2 priors illustrate how different β values affect the onset of acceleration, the presence or absence of matter domination, and the emergence of coupled-scaling regimes. The work highlights that while weak/moderate NMC tends to preserve LCDM-like chronology, strong coupling can significantly alter the intermediate history or drive the system toward H → 0, underscoring DESI DR2's relevance for testing evolving dark energy scenarios in scalar-tensor frameworks.

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 Poincaré 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.

Figures (19)

• Figure 1: Phase space evolution of the dynamical system \ref{['eq:DSfinal']} (without radiation) for specific models considered in this article for $\beta=-10^{-1}$ and DESI DR+CMB+Pantheon+ free parameters/initial conditions: (a) Axions/ALPs, (b) Cyclic ekpyrotic, (c) Exponential+$\Lambda$, (d) Quintessence for $n=-1$, (e) Quintessence for $n=-2$, (f) SFDM. Green region denotes the accelerated expansion phase.
• Figure 2: Evolution of the NMC axions/ALPs model in the slow-roll approximation for Planck 2018 initial data.
• Figure 3: Evolution of the NMC axions/ALPs model in the non-slow-roll CPL approximation for Planck 2018 initial data.
• Figure 4: Evolution of the NMC axions/ALPs model in the non-slow-roll CPL approximation for DESI+CMB+Pantheon+ initial data.
• Figure 5: Evolution of the NMC cyclic ekpyrotic model in the slow-roll approximation for Planck 2018 initial data.