The Shrinking-Matter (SM) Model: A Maximally Self-Sufficient Dynamical Framework for Cosmology

Manuscript Abstract The standard \LambdaCDM model, while empirically accurate, suffers from profound conceptual incompleteness, relying on unexplained Dark Energy (\Lambda) and Cold Dark Matter (CDM) constituents. We introduce the Shrinking-Matter (SM) Cosmology as a structurally superior and maximally self-sufficient alternative. The SM model replaces the dynamic spacetime postulate with the postulate of a globally static background metric (\tilde{g}_{\mu\nu}) in which all dimensional matter, energy, and fields undergo an irreversible scale evolution (shrinkage) governed by a fundamental Scalar Scale Field (\Phi). We demonstrate the Kinematic Invariance of all local physics between the static (SM) frame and the expanding (\LambdaCDM) frame via a conformal transformation, g_{\mu\nu}^{\text{CDM}} = \Omega(t)^2 \tilde{g}_{\mu\nu}, requiring that all dimensional constants scale proportionally to \Omega(t) to preserve fundamental dimensionless couplings (\alpha, \mu) across cosmic time. This framework achieves a structural unification wherein Dark Energy, Dark Matter, and the Arrow of Time emerge as kinematic consequences of the \Phi field dynamics. Crucially, the model derives the Dark Matter mass (M_{\Phi}) as a cosmological necessity, and the Dark Matter self-coupling (g_{\Phi}) is internally fixed by the required stability of galactic halo soliton cores. Furthermore, the CMB homogenization is linked to a dynamic viscous damping process (avoiding inflation), initialized by conditions derived from the Conformal Coherence of the past boundary, and the model predicts unique, falsifiable observational signatures in the Cosmic Microwave Background (CMB) power spectrum. Final Acknowledgment for the USSM Paper The author is the sole progenitor and conceptual architect of the Scale Duality Principle and the Unified Scale-Symmetry Model (USSM). All core postulates, interpretations, and conclusions are the sole responsibility of the author. The author gratefully acknowledges the indispensable assistance of Google’s Gemini Large Language Model (accessible via the conversational interface) as a computational and editorial tool for the following tasks: Formal Derivations: Verifying the mathematical basis of Kinematic Invariance and deriving the necessary scaling of fundamental constants, including \mathbf{G} \propto \mathbf{\Omega^{-2}} and \mathbf{h} \propto \mathbf{\Omega}. Manuscript Structuring: Assisting in the organization, logical flow, and refining the formal, academic language used in the paper.