This work develops a cosmological framework in which gravitational dynamics emerge from the renormalization group (RG) flow of an underlying field-theoretic structure, within the broader program of Information Flow Theory (IFT). Building on the foundations established in IFT-1 (conceptual framework) and IFT-2 (spectral emergence of geometry and physical scales), we show that the RG scale is not an external parameter but is dynamically determined by the spectral properties of spacetime. In a homogeneous and isotropic universe, this leads to an effective relation between the RG scale and the Hubble parameter, schematically: k ~ H As a consequence, the gravitational couplings become dynamical quantities: G = G (H), Lambda = Lambda (H) and the effective gravitational equations acquire additional terms encoding the backreaction of the RG flow. We derive the modified field equations from a scale-dependent effective action and compute explicitly the RG-induced tensor Theta₌ₔ ₍ₔ in a cosmological (FLRW) background. This leads to a closed system of modified cosmological equations, including generalized Friedmann and Raychaudhuri equations, together with a modified conservation law describing energy exchange between matter and the RG sector. A central result of the paper is the emergence of a new dynamical correction to the expansion of the universe, leading to a modified Friedmann equation of the form: H² = (8π G (H) /3) ρ + Lambda (H) /3 + γ (H) H³ This correction arises directly from the internal structure of the RG flow and does not require the introduction of additional fields. It therefore provides a concrete and testable signature of the framework. More generally, the analysis shows that: accelerated expansion can emerge in the ultraviolet regime without an inflaton field, standard cosmology is recovered when the running of couplings becomes negligible, late-time acceleration can arise as an infrared effect of the RG flow, dynamical instabilities associated with flow saturation may provide a mechanism for the emergence of structure. The present work focuses on the theoretical construction and derivation of the effective dynamics. A detailed analysis of observational consequences and constraints will be presented in a dedicated companion paper.
Nicolas Lépinay (Tue,) studied this question.