We develop a covariant and variational formulation of the Information Flow Cosmology (IFC) framework, extending its original renormalization group description of cosmic evolution into a fully geometric setting. In IFC, cosmological dynamics is governed by a beta function controlling both the expansion rate and the production of entropy. In this work, we provide a covariant interpretation of this quantity as a scalar measure of information production, defined through the derivative of an effective entropy along a congruence of observers. This formulation leads to a covariant flow equation for the expansion scalar, providing a geometric description of information-driven dynamics. We show that consistency with the Raychaudhuri equation imposes a non-trivial constraint linking information production to spacetime curvature. By invoking the Einstein field equations, we further demonstrate that the beta function is constrained by the matter content and the expansion of the Universe. We also construct a minimal covariant action, consistent with effective field theory principles, from which the flow equation can be derived. This variational formulation provides a unified framework in which geometry, dynamics, and information flow are encoded within a single scalar structure. This work establishes IFC as a self-consistent covariant effective framework and represents an intermediate step toward a more fundamental information-based theory of spacetime dynamics.
Nicolas Lépinay (Mon,) studied this question.