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

This work introduces Quantum–Kinetic Dark Energy (QKDE), a minimal extension of late-time cosmology that keeps General Relativity intact while allowing the kinetic “normalization” of a single scalar field to drift gently with cosmic time. By construction, the usual linear-scale gravity tests look exactly like standard gravity: gravitational slip is absent, light bending and matter clustering match General Relativity, and gravitational waves still move at light speed with an unchanging effective Newton’s constant. Any departures show up only through the expansion history and the way structure grows over time. I explore two simple ways the kinetic term can evolve—one tied to background curvature, one with a slow, smooth running—and provide a reproducible pipeline for distances, growth-rate forecasts, and survey-oriented observables. The framework is deliberately falsifiable: if linear-scale gravity deviates from its standard behavior, QKDE is ruled out.