Cosmic Expansion without Dark Energy: A Dynamical‑Topological Model with Multiple Metrics

We develop a dynamical‑topological model in which cosmic expansion is not the result of a physical stretching of spacetime but emerges from transitions within a hierarchy of genealogically nested topoi, each equipped with its own metric. In this framework, the observed acceleration of the universe is reinterpreted as a metric effect generated by structural refinement rather than by a new form of energy. The model provides an alternative to dark energy, establishes conceptual connections to Finsler cosmology, and introduces a novel mathematical architecture for understanding large‑scale cosmic dynamics. We argue that this approach clarifies the metaphysical status of spacetime geometry as an emergent, level‑dependent structure and offers a coherent explanation of cosmological acceleration without modifying the field equations of general relativity.