Cosmological Evolution from the Big Bang to the Present: A Unified AMDCF-CSD Simulation of Cosmic Expansion

Simulating the entire history of the universe—from the initial Big Bang singularity to the present-day expanded state—requires robust numerical control over extreme energy gradients that typically cause computational blow-up. In this study, we extend the Adaptive Memory-Driven Coupling Framework with Critical Slowing Down (AMDCF-CSD) to a 2D cosmological domain. The simulation captures three distinct cosmic epochs: (1) the initial thermal explosion, where the AMDCF safety valve dynamically bounds the singularity, acting as a mathematical analogue to cosmic inflation; (2) the cooling phase, during which quantum fluctuations are injected to seed large-scale structures; and (3) the present state, where the universe has expanded into a homogeneous, low-density background. A sponge-layer boundary condition is implemented to emulate the open expansion of space, preventing artificial reflections. The results demonstrate that the AMDCF-CSD kernel successfully stabilizes the entire cosmic timeline without numerical divergence, from the Planck-scale singularity to the large-scale structure we observe today. This work highlights the framework's universality across all scales of physics and offers a novel computational approach to cosmological modeling.