This paper presents the next evolutionary step of the Fundamental Time Theory (FTT), establishing a rigorous low-energy Effective Field Theory (EFT) framework for the dynamic time-field Phi. While standard cosmological models (Lambda-CDM) are facing an unprecedented crisis due to the statistically significant Hubble (H0) and growth of structure (S8) tensions, this work introduces a simultaneous resolution to both anomalies without introducing ghost instabilities or violating causality. Key Features of the Model: Kinetic Capturing (K-mouflage): By utilizing a non-linear kinetic function, the model locks the effective sound speed of perturbations into a strictly subluminal regime, inherently screening the scalar field in high-density environments and neutralizing quantum ghosts. Autocatalytic Late-Time Acceleration: The field evolves within an asymmetric potential featuring a cubic autocatalytic driving force. Numerical background simulations show that its activation at redshift z less than 0.7 drives the dark energy equation of state into a controlled phantom regime, organically lifting the local expansion rate to H0 = 72.9 km/s/Mpc. Structure Growth Suppression: Through a direct coupling parameter Beta to cold matter, the dynamic field relaxes the clustering of matter in the late epoch, pulling the theoretical S8 value down into perfect alignment with weak-lensing data. Asymptotic Cosmic Safety: In contrast to standard phantom dark energy models that end in a catastrophic Big Rip singularity, a quartic stabilizing term bounds the potential from below, ensuring a smooth future transition into a stable de Sitter vacuum. This preprint includes the full Lagrangian derivation, stability analysis, and the numerical background simulation dataset. It builds upon and mathematically consolidates the conceptual foundations laid out in previous FTT publications (Strmsek, 2025).
Klemen Strmšek (2026) studied this question.