What question did this study set out to answer?

The aim is to develop a minimal dark energy framework that incorporates time-dependent scalar kinetic normalization.

February 16, 2026

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

Key Points

The aim is to develop a minimal dark energy framework that incorporates time-dependent scalar kinetic normalization.
Developed the Quantum-Kinetic Dark Energy (QKDE) framework with a time-dependent scalar kinetic normalization.
Maintained the unmodified Einstein–Hilbert metric structure while introducing a covariantly completed clock field.
Conducted numerical simulations to validate the background equations of the framework.
Analyzed scalar perturbations and their influence on growth via the Einstein equation.
Obtained a closed first-order background system in e-fold time with specific propagation characteristics for scalar perturbations.
Formulated the scalar-field equation as an exchange equation with the clock sector.
Demonstrated that observable signatures depend solely on expansion history and induced growth.
Provided a numerical pipeline for reproducibility and established sharp, falsifiable predictions about linear scales.

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 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.

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