A Phenomenological Model of Hierarchical Density Transitions Across Cosmic and Astrophysical Scales

The paper develops a phenomenological model aimed at conceptually unifying the hierarchical structure of matter across a tremendous range of scales, extending from the vast, observable cosmos down to the subatomic and speculative ultimate quantum limits. It operates on the profound idea that simplified, universal rules might govern the formation and transition of all observed structures. It proposes a single recursive power-law formula to describe how density transitions occur between distinct physical layers. The model is built entirely upon core suppositions derived solely from physical principles, intentionally avoiding any reliance on empirical fitting. These foundations include the idea that geometric scaling is fractal across large structures; that high-density transitions are threshold-driven by critical values like the Jeans density or nuclear saturation density, mimicking a phase change; and that immense density jumps are energy-biased, requiring a huge multiplier calculated from the ratio of binding energy (like fusion or nuclear force) to gravity. The primary conclusion is that this framework achieves conceptual unification, successfully integrating mechanisms from cosmology, astrophysics, and particle physics under a common law of geometry, threshold activation, and energetic bias. However, the model explicitly concludes that its quantitative precision is minimal, confirming its role as a mechanism-driven analogy rather than a rigorous predictive theory, yet providing a powerful tool for analyzing the underlying principles governing the universe’s structure.