The Fabric Constituted by E = mc² : A Rigorous Framework for Spacetime as an Energetic Medium with Regional Vibrational Modes

We propose a rigorous theoretical framework in which the fabric of spacetime itself is fundamentally constituted by energy. In this view, mass–energy equivalence is not treated merely as a conversion rule, but as the ontological foundation of spacetime structure. This energetic medium supports regional vibrational modes, described by a scalar field that couples to spacetime curvature and to the distribution of matter.

Through a systematic construction based on effective field theory and respecting diffeomorphism invariance, we derive the governing field equations from first principles. We carry out a comprehensive stability analysis, explicitly addressing the instabilities typically associated with higher-order dynamics, and demonstrate that the framework remains mathematically consistent within the observable cosmological regime. The proposed vibrational field, characterized by an extremely small effective mass scale, leads to concrete and testable signatures in the large-scale structure of the Universe. These include a measurable enhancement in the galaxy two-point correlation function on very large scales, a quasi-periodic spacing of cosmic voids, and distinctive features in the angular power spectrum of the cosmic microwave background.

We perform a full Bayesian model comparison using current galaxy survey data and precision measurements of the cosmic microwave background. The resulting Bayesian evidence indicates that the framework is neither strongly favored nor decisively ruled out when compared with the standard cosmological model. Definitive tests are expected from forthcoming large-scale surveys, which will either confirm the vibrational paradigm with high statistical significance or place stringent constraints that effectively falsify it. Overall, this work demonstrates how creative physical intuition—specifically, the analogy between cosmic structure and acoustic patterns—can be developed into a rigorous and falsifiable theoretical framework through the systematic application of effective field theory methods, stability analysis, and quantitative observational predictions.