his work introduces a novel framework in which the cosmological evolution of the Universe is described as an effective renormalization group (RG) flow arising from the coupling between matter and geometry in Entangled Relativity. Starting from the Friedmann equations, we demonstrate that the dynamics of the Hubble parameter can be reformulated in terms of a cosmological beta function, directly linked to the effective equation of state of the Universe. This provides a concrete realization of RG concepts in a gravitational context. A minimal model of matter–geometry coupling leads to a modified RG flow equation, predicting a maximal Hubble scale and the absence of a finite-time cosmological singularity. The early Universe is reinterpreted as an asymptotic high-curvature fixed point, naturally giving rise to an inflationary phase without introducing additional scalar fields. The framework also establishes a deep connection between cosmology and thermodynamics, with the monotonic growth of horizon entropy playing the role of a cosmological c-function. This suggests that cosmic time itself may emerge from the RG flow. The model reproduces standard cosmological behavior at low curvature while predicting testable deviations at high redshift and during inflation. Constraints from observational data provide bounds on the matter–geometry coupling. This paper constitutes the first step of a broader program aiming to establish cosmology as an emergent renormalization group phenomenon.