Ultraviolet Curvature Saturation and Residual Infrared Vacuum

We present a unified geometric framework in which the observable cosmological vacuum sector emerges as the causally filtered residue of a primordial ultraviolet curvature background. Building upon a regularized spacetime geometry characterized by a universal Planckian curvature saturation scale K_UV ~ l_p^-2, we investigate how the growth of the cosmological causal horizon projects this ultraviolet sector into an effective infrared vacuum component. The filtering process is governed by the horizon scale R_H(t) = c/H(t), leading to the effective curvature relation K_eff(t) = K_UV (l_p/R_H(t))^2. As the observable Universe expands, the causal filtering mechanism progressively suppresses the admissible infrared curvature sector, naturally generating the observed vacuum curvature scale K_eff ~ 10^-52 m^-2 at the present cosmological epoch. To provide a