Radial Coherential Dynamics as Ghost-Free Hilltop Quintessence: FRW Solutions and Observational Constraints RCD Hilltop Dark Energy Series — Paper I

Paper I of the RCD Hilltop Dark Energy Series. We investigate the cosmological dynamics of a scalar field model motivated by Radial Coherential Dynamics (RCD), in which a coherence parameter C ∈ (0,1) evolves with a non-canonical kinetic coupling K(C) = (1−C)² and a symmetric potential V(C) = vC(1−C). Working in the ghost-free convention with positive-definite kinetic energy, we establish that the model belongs to the class of k-essence theories linear in X, with sound speed c²_s = 1 identically. We demonstrate that C = 1/2 is an unstable equilibrium of the potential. For initial conditions C₀ ∈ [0.42, 0.51] near the hilltop, the model produces viable dark energy with w₀ ∈ [−1.00, −0.81] and Ω_DE ≈ 0.685, placing it in the thawing quintessence class.