Covariant Field Equations and Causal UV--IR Filtering in a Regularized Curvature Framework

This work presents a covariant geometric framework connecting a saturated ultraviolet curvature scale with the observable infrared vacuum sector through a causal filtering mechanism.

The model assumes the existence of a finite Planckian curvature bound, replacing divergent ultraviolet behavior with regularized finite-curvature geometric cores. The observable vacuum sector is interpreted as an effective infrared residue associated with the finite causal domain accessible to a cosmological observer.

A local covariant formulation is developed using auxiliary geometric fields, leading to modified field equations derived from an effective action while preserving general covariance and the contracted Bianchi identities.

The framework naturally produces an effective vacuum density that evolves approximately as H², without introducing additional matter fields, quintessence sectors, or phenomenological vacuum-running parameters. In this interpretation, the observed vacuum energy is not treated as an independent fundamental component but as a geometric consequence of the relationship between the Planck scale and the cosmological causal scale.

The paper should be regarded as an effective geometric description of the observable causal domain. The microscopic origin of the proposed ultraviolet–infrared projection law, together with its possible extension beyond the observable horizon, remains an open problem for future investigation.