This work develops a universal theoretical framework for cosmological evolution based on renormalization group (RG) concepts. Within the context of Entangled Relativity, we show that the dynamics of a homogeneous Universe can be reformulated as an RG flow governed by a cosmological beta function. A central result is that this structure is universal: under general assumptions such as locality, smooth evolution, and the dominance of a single scale, the beta function takes a factorized form depending only on the Hubble parameter. This establishes cosmological evolution as belonging to a universality class of RG flows. We further demonstrate the existence of a monotonic entropy function associated with the cosmological horizon, providing a cosmological analog of a c-theorem. This identifies entropy as a fundamental quantity controlling the irreversibility of the evolution. The framework also reveals structural connections with conformal field theories, suggesting that cosmology may be understood within a broader RG universality framework rather than through specific microscopic models. This paper constitutes the second step in a program aimed at formulating cosmology as an emergent renormalization group phenomenon.