Forced GUT Hamiltonian Limit For Cosmological RG Flow in the Stochastic High Energy Limit

We demonstrate that the approach to the balance manifold dynamically suppresses curvature contributions, yielding an effectively flat universe without requiring fine-tuned initial conditions or a turning point in the evolution. Inflation corresponds to a regime of entropy imbalance along the scale-flow trajectory, and its termination occurs naturally as the system reaches balance, without the need for engineered exit mechanisms, additional fields, or potential features. While the full mathematical structure of this result is developed within Newell’s stochastic framework, its cosmological interpretation is most transparently understood through the logarithmic gauge mapping inherent to the entropy-controlled evolution. This establishes the entropy clock as the minimal and physically natural description of early-universe dynamics in the Forced GUT setting. We show that within Newell’s stochastic Forced Grand Unification (Forced GUT) framework, accelerated expansion, spatial flatness, and exit from the inflationary regime arise as structural consequences of entropy-driven scale flow rather than from tuned dynamics or engineered model ingredients. The framework is governed by a stochastic controller whose natural evolution parameter is a logarithmic renormalization variable, σ=ln⁡(μ/μc), describing relaxation toward an entropy-balance (unification) manifold. In this formulation, the logarithmic growth of the scale factor, N=∫Hdt=ln⁡(af/ai), is shown to be purely kinematic, following directly from H=a˙/a, while the physical evolution is controlled by flow in σ.Moreover, in the high-energy limit, the relevant evolution parameter is logarithmic in scale and does not require dynamical normalization to be well-defined.