A Covariant Vacuum Field Framework for the Effective Evolution of Fundamental Constants

Preprint. This manuscript is a preprint and has not been peer-reviewed. It is currently under consideration for publication in a peer-reviewed journal AbstractWe present a covariant field-theoretic framework in which the effective evolution of gravitationaland cosmological parameters emerges from vacuum dynamics rather than from explicit variationsof fundamental constants. The theory is formulated at the level of a generally covariant action,possesses well-defined field equations, and admits a consistent Hamiltonian (ADM) formulation. Inappropriate limits, the framework reduces smoothly to general relativity with a cosmological constant.The construction is explicitly effective in nature and is intended as a controlled theoretical settingfor analyzing vacuum relaxation, cosmological evolution, and the late-time stability of physicalparameters within classical and quantum gravity.