Kinetic Extensions of RCD: Structural Limits of Kinetic Stabiliza- tion for Hilltop Quintessence RCD Hilltop Dark Energy Series — Paper II

We investigate whether kinetic modifications to the Radial Coherential Dynamics (RCD) scalar field model can stabilize the hilltop at C= 1/2, which was shown to be linearly unstable in the ghost-free formulation of Paper I. We consider three extensions of increasing strength: (i) a quadratic correction P= K(C)X+ αX2 −V(C), (ii) a DBI resummation P=−f−1√1−2fX+ f−1 −V with f= K, and (iii) a generalized DBI structure P=−F−1√1−2FKX+ F−1 −V with an independent warp factor F. We prove that no kinetic modification of any form — perturbative or resummed — can change the linear stability of a potential hilltop, because the linearized equation of motion at a stationary point (˙ C= 0) depends only on the potential curvature V′′and the kinetic coefficient at zero velocity, both of which are independent of nonlinear kinetic structure. Numerical integration confirms that even with extreme DBI friction (γmax >200, warp factor F = 104), the field eventually escapes the hilltop. We identify a matching subtlety in the standard DBI formulation and show that the correct low-energy limit requires a two-parameter extension (the warp factor F decoupled from the kinetic coupling K). The results establish a no-go theorem for kinetic stabilization of hilltop quintessence within k-essence, and motivate either potential modifications or coupling to additional sectors as paths forward.