The Scale-Divergence Problem: A Foundational Schism in Modern Cosmology

This document provides a rigorous examination of the Scale-Divergence Problem, a fundamental schism in modern cosmology that arises from the antithetical performance of the two leading theoretical frameworks—Lambda Cold Dark Matter (ΛCDM) and Modified Newtonian Dynamics (MOND)—across different physical scales. ΛCDM achieves remarkable success in explaining cosmological observations (Cosmic Microwave Background, large-scale structure) but encounters significant challenges at galactic scales (cusp-core problem, radial acceleration relation). Conversely, MOND provides a simple, parameter-minimal explanation for galactic dynamics but fails catastrophically at cosmological scales and in galaxy clusters. This analysis systematically evaluates the theoretical foundations, observational successes, and critical failures of both paradigms. It demonstrates that neither framework, in its current form, offers a complete and universally consistent description of gravitational phenomena across all scales. The document further examines emerging hybrid models (such as Superfluid Dark Matter) that attempt to bridge this schism, and identifies critical observational tests that could resolve this foundational tension. The resolution of the Scale-Divergence Problem—whether through refinement of ΛCDM, development of a relativistic MOND, or emergence of a novel synthesis—represents one of the most profound challenges in contemporary physics, with implications for our fundamental understanding of gravity, dark matter, and the evolution of cosmic structure.