Unification of Cosmological Evolution: From the Planck Scale to the Asymptotic Regime — A Unified Scaling Description Governed by ε(t) within Standard Physics

Abstract

This work develops a minimal formalism that unifies cosmological evolution and diverse physical domains through a set of interconnected relations and a single underlying scaling structure.Within this framework, global properties of the Universe emerge directly from established physical laws, without additional degrees of freedom, and remain consistent with observations and independent cosmological estimates.Version 2 (revised):This version introduces minor clarifications and structural refinements, with particular emphasis on the dynamical sector and the distinction between local and global normalization. The formalism, results, and conclusions remain unchanged. Version 3 (Compact manuscript): This manuscript is a compact version of the extended work previously published on Zenodo.It should therefore not be read as a separate new study, but as a shorter, more concise, and more focused presentation of the same formal framework.The main formal structure, theoretical framework, and central conclusions of the extended work are preserved.The compact version focuses on the essential aspects of the formalism in order to present its core structure in a shorter, clearer, and more focused form. Version 4 (Compact manuscript, revised): This final compact version presents a formally and methodologically refined formulation of the proposed cosmological framework, in which a single dimensionless parameter organizes global relations across physical domains and cosmological epochs on a fixed Planck reference basis. The underlying structure is derived from established physical relations without introducing new fields, particles, additional degrees of freedom, or varying fundamental constants. The manuscript also outlines the potential of the formalism for further theoretical and observational application.