Stabilizing descending dark energy via non-minimal scalar-curvature coupling: an exploratory dynamical systems approach

We investigate a novel extension of the Quintessence-Driven Slow-Contraction (Q-SC-CDM) model by introducing a non-minimal coupling (NMC) between the scalar field and the Ricci scalar of the form ξ φ ² R ξ ϕ 2 R . Recent studies have suggested that while descending dark energy models can facilitate a transition to a slow-contraction phase, they often lack stable late-time attractors unless specific potential symmetries are assumed. By performing a rigorous dynamical system analysis, we demonstrate that the inclusion of the NMC parameter ξ ξ provides the necessary degrees of freedom to stabilize the dark energy-dominated era without the requirement of fine-tuned potential slopes ( $$M=m$$ M = m ). Our numerical results show that the model remains consistent with current observational constraints ( wφ ≈ -1 w ϕ ≈ - 1 ) while predicting a smooth transition to a “stiff” matter phase ( $$w > 1$$ w > 1 ) in the near future. This work provides a robust theoretical bridge between observed cosmic acceleration and cyclic cosmological scenarios.