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

We present the high-energy, early-universe formulation of the -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 10^-36 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 -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 crosses the unity threshold (1), the field exits the inflationary regime and undergoes a phase transition.