The Primordial Quantum Dawn of the $\Psi$-Field: Stochastic Inflation, Reheating, and the Origin of the Cosmic Damper

We present the high-energy, early-universe formulation of the $\Psi$-field cosmological model, extending the framework from a classical macroscopic damper to a primordial quantum scalar field. By analyzing the system in the ultra-high energy regime ($t \approx 10^{-36}\text{ s}$), we establish the stochastic Klein-Gordon equation under the influence of quantum fluctuations, modeled as a Gaussian white noise framework. Numerical integration utilizing the Euler-Maruyama method demonstrates that the $\Psi$-field naturally sustains a stable slow-roll inflationary phase lasting exactly $60.00$ e-foldings. This precise duration successfully satisfies the cosmological horizons and flatness constraints without fine-tuning. Crucially, as the slow-roll parameter $\epsilon$ crosses the unity threshold ($\epsilon \ge 1$), the field exits the inflationary regime and undergoes a phase transition.