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 αB = αM = αT = αH = 0, implying luminal tensor propagation and a constant Planck mass. From this action, a closed first-order background system in N = a is obtained. Scalar perturbations propagate with sound speed cₛ² = 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 + 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 cT² = 1. Any observational departure from these null tests lies outside the QKDE baseline and would rule out the model.