Evading Cosmological Strong Coupling in Non-minimally Coupled Vector Gravity

Recent analyses of Proca theories with non-minimal curvature couplings have uncovered an additional scalar degree of freedom with an identically vanishing propagation speed, c s 2=0, signaling a scale-dependent strong-coupling problem. In this Letter, we show that an additional derivative interaction can lift this zero-speed degeneracy and restore a non-degenerate quadratic dynamics for the scalar perturbations. In an open region of parameter space, the scalar kinetic matrix is positive definite and the high-frequency propagation speeds are real and positive. At quadratic order, this removes the specific signature of strong coupling associated with the c s 2=0 mode. We also uncover a non-uniform limit as the temporal vector condensate approaches zero: at fixed nonzero A 0, the formal extreme-ultraviolet regime develops a ghost, while the kinetic structure of the exactly vanishing-condensate branch is different. The momentum scale at which this ghost appears is pushed toward increasingly high values as A 0 to0. Whether the ghost scale ultimately lies above the EFT cutoff depends on an independent determination of the EFT cutoff. Finally, we identify a stable de Sitter fixed point with A 0 not equal to0, surrounded by a finite region in which the scalar no-ghost and high-frequency stability conditions remain satisfied.