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

Abstract 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 $$\xi \phi ^2 R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> . 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 $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> provides the necessary degrees of freedom to stabilize the dark energy-dominated era without the requirement of fine-tuned potential slopes ( $$M=m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> ). Our numerical results show that the model remains consistent with current observational constraints ( $$w_{\phi } \approx -1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>w</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ) while predicting a smooth transition to a “stiff” matter phase ( $$w &gt; 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>w</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ) in the near future. This work provides a robust theoretical bridge between observed cosmic acceleration and cyclic cosmological scenarios.