A Minimal Specified Realization of Relativistic Coherent Vacuum Gravity Theory

This work presents a minimal specified realization of Relativistic Coherent Vacuum Gravity Theory (rCVGT), providing a self-consistent theoretical framework for cosmological applications.

The model is formulated at the level of a covariant scalar–tensor action, in which gravitational dynamics arise from a vacuum coherence field, a physical time-rate field, and their dynamical interaction through a coherence–time locking mechanism. From this action, we derive the field equations, background cosmology, and perturbative structure required for connection to observable cosmology.

The construction is intentionally minimal and represents a controlled truncation of the full rCVGT theory space. The purpose is to obtain a mathematically closed and observationally testable realization while retaining the essential physical ingredients of the theory, including vacuum coherence, time-rate dynamics, and modified gravitational response.

This work provides the theoretical foundation for subsequent numerical implementation and observational analysis. In particular, a companion paper presents the numerical pipeline and comparison to large-scale structure data, while additional technical notes develop the perturbation framework and outline Boltzmann solver implementations.

Together, these works establish a coherent program connecting the covariant rCVGT framework to modern cosmological observations.