The T–VRF Unified Field Theory — A Symmetry-Protected Unified Dark Sector with Emergent Time

The T–VRF Unified Field Theory introduces a two-scalar-field framework that unifies dark matter, dark energy, and early-time interaction phenomena within a single symmetry-protected model. The theory is built around a time-field T, responsible for late-time accelerated expansion, and a vacuum resonance field \phi, which behaves as cold dark matter in its oscillatory regime. The model incorporates a shift-protected interaction term W(T,\phi) that modulates the effective mass of the vacuum resonance field and allows for controlled early-time deviations, including EDE-like behaviour and mathematically defined “time-fold” events in the evolution of the time-field. This paper presents the full theoretical framework, complete background dynamics, linear perturbation theory, full stability analysis, cosmological behaviour, observational predictions, and technical appendices containing full derivations and parameter classifications. The T–VRF model provides a unified, technically natural, and observationally testable extension to ΛCDM.