The Fundamental Cosmological Equation: A Covariant Field-Theoretic Realization of the Odero Axiom
Year: 2026
Type: preprint
Abstract: We present the Fundamental Cosmological Equation, 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 within a Riemannian spacetime manifold, we derive modified Einstein field equations from an action principle. The cosmological expansion dynamics are governed by the Fundamental Cosmological Equation. Under this formulation, cosmic acceleration emerges naturally from the dynamical evolution of an information-mediated control field φ(xμ) without requiring a bare cosmological constant Λ. The framework further introduces an information-mediated gravitational coupling through the bounded control function C(φ), connecting structural order to the effective gravitational influence of matter. A microfoundational statistical-mechanical interpretation of the information field is established through coarse-grained entropy, relative entropy, and Kullback-Leibler divergence, providing a thermodynamic basis for the field dynamics. We establish field equations, inter-species conservation laws, FLRW reduction, stability conditions, falsifiable observational signatures, proposed numerical methodologies, and current limitations of the model.
Author: Odero, John Otieno
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203710400
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