The Breathing Universe: 208Horizon-Scale Regulation of Vacuum Energy

This work develops a phenomenological interpretation of the cosmological constant within the framework of the Breathing Universe Model (BUM). The central proposal is that the observed vacuum curvature does not arise directly from the unrestricted microscopic sum of quantum vacuum contributions, but instead emerges as the finite large-scale residual of incomplete vacuum balancing across horizon-limited coherence domains. Within the framework, the vacuum is interpreted as a dynamically organized coherence structure containing complementary delocalizing and localizing redistribution tendencies. Local vacuum organization approaches an approximate zero-line balance condition, while exact global cancellation remains impossible because causal coordination is limited by the cosmological horizon. The observable cosmological constant is therefore interpreted as the residual curvature generated by incomplete statistical balancing across the maximal coherence domain of the observable universe. This interpretation leads naturally to the phenomenological scaling relation: ΛBUM = ξ RH^ (-2), where RH denotes the cosmological horizon radius and ξ is a dimensionless parameter characterizing the efficiency of incomplete horizon-scale vacuum balancing. Expressed in Planck units, the relation becomes: ΛBUM lP² = ξ (lP / RH) ², which naturally generates the observed cosmological hierarchy: Λ lP² ~ 10^ (-122). Within this perspective, the extreme smallness of the cosmological constant is interpreted not as the result of exact microscopic fine tuning, but as a structural consequence of the enormous separation between minimal Planck-scale coherence structure and maximal horizon-scale causal organization. The framework remains fully compatible with standard ΛCDM cosmology at leading order and does not modify the Einstein field equations or Friedmann expansion dynamics. Instead, it provides a coherence-based interpretation of cosmological vacuum curvature linking vacuum structure, horizon-scale regulation, entropy-related suppression, and large-scale cosmological organization within a unified phenomenological framework.