Dissolution of the Vacuum Energy Problem in an Integral-Based Ontology: The 0-Sphere Model Perspective

Description [32 Essential] The cosmological constant problem—an over 120-order-of-magnitude discrepancy between theoretical vacuum energy density and observational bounds—arises from standard field-theoretic assumptions that treat local quantum fields as fundamental, with zero-point energies at each spacetime point summing to a gravitationally relevant vacuum energy. This work proposes that the problem is dissolved, not resolved, by adopting an integral-based ontology within the 0-Sphere model. In this framework, fundamental entities are proper-time–parametrized worldline processes, while spacetime and local fields emerge as effective descriptions of accumulated phase histories. Conventional vacuum energy, defined as an infinite sum over local zero-point modes, never arises as a well-posed physical quantity; only energies associated with open, exchangeable processes contribute to gravitational dynamics. Consequently, the cosmological constant problem—as traditionally formulated—does not arise. Local quantum fields remain operationally useful for scattering and effective interactions, but assigning zero-point energies to each mode is not part of the fundamental ontology. This clarifies the hierarchy underlying quantum field theory and general relativity: physical observables correspond to integral quantities, while fields and spacetime are emergent. The framework admits a clear empirical test: any observation of direct gravitational effects from vacuum fluctuations distinct from phase accumulation would directly challenge it. The small observed cosmological constant remains an open question, potentially reflecting boundary conditions, collective phenomena, or new physics. This work complements the connection-based trilogy (Parts I–III, Zenodo 2025–2026) by demonstrating that integral-based observables naturally dissolve conceptual difficulties in local field formulations, providing a coherent geometric foundation in which histories, connections, and accumulated phases constitute physical reality. Keywords 0-Sphere model Cosmological constant problem Vacuum energy Integral-based ontology Line integrals emergent gravitational-like behavior line-integral based gravity geometric phase and phase accumulation internal phase synchronization Zitterbewegung dynamics energy conservation and redistribution proper time emergence connection-based formulation no additional force mediators comparison with Einstein field equations