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

Abstract

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 \chi such that K = K(\chi) > 0, while the Einstein-Hilbert metric sector remains unmodified. The resulting effective action admits a diffeomorphism-invariant completion, and working in unitary gauge \chi = t reproduces the background equations used in the numerical analysis. Within the effective field theory of dark energy (EFT-DE) description the model corresponds to \alpha_K > 0 with \alpha_B = \alpha_M = \alpha_T = \alpha_H = 0, implying luminal tensor propagation and a constant Planck mass. Scalar perturbations propagate with c_s^2 = 1, satisfy \Phi = \Psi, and source linear growth through the unmodified Einstein equations. Observable signatures therefore arise solely through the expansion history H(a) and the induced growth D(a). Two realizations of the kinetic normalization are studied: (i) a curvature-motivated form K = 1 + \alpha R/M^2, and (ii) a phenomenological running K = 1 + K_0 (1 + z)^p. A reproducible numerical pipeline and Fisher analysis for H(z), distances, and f\sigma_8(z) are presented. The framework predicts \mu(a,k) = \Sigma(a,k) = 1, \eta(a,k) = 0, and c_T^2 = 1 on linear scales, providing clear falsifiable null tests. Earlier drafts circulated under the working title Scalar-Cost Dark Energy (SCDE).