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

This work presents a covariant geometric framework that connects a saturated ultraviolet curvature scale with the observed infrared vacuum sector through a causal UV–IR filtering mechanism.

The central idea is that spacetime possesses a maximum admissible curvature associated with the Planck scale, replacing singular ultraviolet behavior with regular finite-curvature geometric cores. The observed cosmological vacuum is then interpreted as a residual infrared curvature emerging from the projection of this ultraviolet sector onto the finite causal domain accessible to observation.

A local covariant formulation is developed using auxiliary geometric fields, leading to modified gravitational field equations that preserve general covariance and satisfy the Bianchi identities. Within this framework, the effective vacuum sector naturally exhibits running-vacuum behavior without introducing new matter fields, quintessence components, or phenomenological vacuum-running parameters.

The model assumes a single homogeneous and isotropic spacetime and does not require physical boundaries, multiple spacetime regions, or discontinuities at cosmological horizons. The causal horizon is interpreted only as the scale defining the observable domain relevant to the effective geometric description.

The framework is proposed as an effective theory associated with the observable causal sector of the Universe. The microscopic origin of the UV–IR projection law and its possible extension beyond the observable horizon remain open questions for future investigation.