Quantum–Kinetic Dark Energy (QKDE): An effective dark energy framework with a covariantly completed time-dependent scalar kinetic normalization

A minimal, effective dark-energy framework–Quantum–Kinetic Dark Energy (QKDE)-is developed in which the scalar kinetic normalization carries a slow background time dependence through a covariantly completed clock field [Formula: see text] such that [Formula: see text], while the Einstein–Hilbert metric sector remains unmodified. The effective action [Formula: see text] admits a diffeomorphism-invariant completion; working in unitary gauge [Formula: see text] reproduces the background equations employed numerically in this work. Within the EFT–DE description this corresponds to [Formula: see text] with [Formula: see text], so tensors are luminal and the Planck mass is constant. Within this effective framework, a closed first–order background system in e–fold time is obtained; scalar perturbations propagate with [Formula: see text], satisfy [Formula: see text], and source linear growth through the unmodified metric Einstein equation. The scalar-field equation takes the form of an exchange equation with the clock sector, while the total energy–momentum tensor is covariantly conserved. All observable signatures therefore enter solely through the expansion history [Formula: see text] and the induced growth [Formula: see text]. Two kinetic normalizations are treated in detail: (i) a curvature-motivated form [Formula: see text], for which an iteration-free algebraic identity for [Formula: see text] is derived; and (ii) a phenomenological running [Formula: see text]. A reproducible numerical pipeline is provided together with a Fisher setup based on exact variational (sensitivity) equations for distances, [Formula: see text], and [Formula: see text]. Stability and admissibility reduce to [Formula: see text] and a nonvanishing algebraic denominator in the curvature case. The framework yields sharp, falsifiable null predictions on linear scales: [Formula: see text]; any statistically significant deviation lies outside the effective QKDE baseline. The framework is interpreted as an effective, unitary-gauge cosmological description arising from a covariantly completed theory, rather than as a manifestly covariant scalar–tensor model written directly in fixed time slicing.