On the Effective Nature and Cosmological Evolution of Fundamental Physical 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 This manuscript is a preprint and has not been peer-reviewed.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. Abstact We develop a covariant field–theoretic framework in which the apparent evolution of gravitationaland cosmological parameters arises from vacuum dynamics rather than from explicit variations offundamental constants. The construction is formulated at the level of a generally covariant action,admits well–defined field equations, and possesses a consistent Hamiltonian (ADM) structure. Ascalar vacuum field is introduced as a coarse–grained degree of freedom encoding the large–scalestate of the vacuum, while matter fields remain minimally coupled to the spacetime metric. Effectivegravitational and cosmological parameters emerge operationally from the vacuum sector and reducesmoothly to constant values in appropriate limits, recovering general relativity with a cosmologicalconstant. The framework is explicitly effective in nature and does not claim fundamental completeness. Emphasis is placed on internal consistency, covariance, and the interpretation of late–timestability of physical parameters as a dynamical vacuum regime. The analysis clarifies the relation ofthe framework to scalar– tensor gravity, vacuum relaxation models, and varying–parameter scenarios, and delineates its predictive content and limitations. The results provide a controlled theoreticalsetting for studying effective vacuum evolution within classical and quantum gravity.