Quantum–Kinetic Dark Energy (QKDE): An effective dark energy framework with the Einstein–Hilbert metric sector intact and a time–dependent scalar kinetic normalization

Quantum–Kinetic Dark Energy (QKDE) is introduced as a minimal, GR-preserving dark energy framework in which only the scalar kinetic normalization carries a background time dependence K(t) > 0, while the Einstein–Hilbert sector remains unmodified. In unitary gauge—where time diffeomorphisms are broken—the action S = ∫ d⁴x √−g [½ Mₚₗ² R + K(t) X − V(φ)] maps exactly onto the EFT of Dark Energy with αₖ = K · (φ̇²)/(H² Mₚₗ²) > 0 and α_B = α_M = α_T = α_H = 0, implying luminal tensor propagation and a constant Planck mass. From this action, a closed first-order background system in N = ln a is obtained. Scalar perturbations propagate with sound speed c_s² = 1, obey the metric-potential equality Φ = Ψ, and preserve the GR linear-growth equation. As a result, all late-time observational signatures arise solely through the modified expansion history H(a) and the induced growth factor D(a). Two explicit realizations of K(t) are analyzed: Curvature-motivated form: K = 1 + α R/M², supported by a fully algebraic, iteration-free identity for K'/K. Phenomenological running: K = 1 + K₀ (1 + z)^p. A complete numerical pipeline is provided—including state-vector choices, integration tolerances, and internal identity checks—along with a Fisher-forecast setup based on exact sensitivity equations for distances, H(z), and fσ₈(z). Stability and physical viability reduce to maintaining K(t) > 0 and avoiding the algebraic denominator zero in the curvature-based model. QKDE yields sharp, falsifiable predictions on linear scales: μ(a, k) = 1, Σ(a, k) = 1, gravitational slip = 0, tensor speed c_T² = 1. Any observational departure from these null tests lies outside the QKDE baseline and would rule out the model.