Information-Driven Gravity II: Scalar–Tensor Derivation from Fisher Information and Statistical Field Theory

This work presents a first-principles derivation of the Information-Driven Gravity framework introduced in the companion paper: Cobham, B. (2026)Information-Driven Gravity: A Unified Framework Resolving Cosmological Tensions. Starting from a statistical manifold of local probability distributions equipped with the Fisher information metric, a partition function over information states is constructed and coarse-grained using Wilsonian renormalization group methods. The resulting effective field theory naturally produces a scalar–tensor modification of gravity consistent with the phenomenological model of Paper I. The derivation shows that: • The information scalar field arises from Fisher information geometry rather than being postulated.• The scalar–tensor action emerges from renormalization of the information partition function.• Chameleon screening appears automatically in high-density environments.• Parameter bounds follow from consistency with the Bekenstein entropy bound.• The theory predicts a constrained potential, a coupling–mass relation, and temperature-dependent running absent in generic scalar–tensor models. This paper serves as the theoretical foundation for the Information-Driven Gravity framework and is intended as a companion derivation to the original phenomenological work. This work is theoretical and has not yet been experimentally verified.