The Fundamental Cosmological Equation: A Covariant Field-Theoretic Realization of the Odero Axiom

We present the Fundamental Cosmological Equation (FCE), establishing a fully covariant cosmological realization of the general persistence framework known as the Odero Axiom (C(I) · E > D). By promoting core persistence quantities, Information (I), Control Efficiency C(I), Usable Energy (E), and Systemic Decay (D), to scalar and tensor field variables on a Riemannian spacetime manifold, we derive modified Einstein field equations from an action principle. Cosmic expansion dynamics are governed by the Fundamental Cosmological Equation. Within this framework, cosmic acceleration emerges naturally from the dynamical evolution of an information-mediated control field φ(xᵘ) without requiring a bare cosmological constant Λ. We derive the associated field equations, inter-species conservation laws, and FLRW cosmological reduction, and discuss stability conditions, observational signatures, proposed numerical methodologies, and current limitations of the model.