The Modular–Elastic Vacuum Theory (TMEV): An Effective Field-Theoretic Framework for Emergent Geometry and Dark Energy

We present the Modular–Elastic Vacuum Theory (TMEV), a self-consistent field-theoretic framework in which the physical vacuum is modeled as a structured medium with internal degrees of freedom. The formalism is defined on a four-dimensional spacetime coupled to a compact internal manifold, allowing a unified description of vacuum dynamics. The theory leads to an effective mass spectrum derived from the internal Laplacian operator, together with a projection mechanism that connects internal modes to observable quantities. In addition, one-dimensional string-like excitations arise naturally as reduced sectors of the vacuum field, without introducing fundamental extended objects. At macroscopic scales, the framework yields an emergent gravitational structure consistent with Einstein-like dynamics. The cosmological constant is interpreted as an effective property of the vacuum rather than a fundamental input parameter. The formulation is mathematically consistent within classical field theory and does not rely on external assumptions beyond the defined vacuum structure.