From Galaxy Rotation to Cosmic Acceleration: A Unified Framework via the Spatial-Material Continuum

This work introduces the Spatial-Material Continuum (SMC) paradigm, a novel theoretical framework that offers a unified explanation for two of the most significant challenges in modern astrophysics: the anomalous rotation curves of spiral galaxies and the accelerated expansion of the Universe. The theory originates from a systematic analysis of the SPARC galaxy catalog, which reveals a precise empirical law where the effective gravitational constant weakens in regions of high density, governed by a single parameter β = 0.0385 ± 0.0048. Strikingly, this measured value coincides with the fundamental geometric constant 1/(8π) from Einstein's field equations. Building on this empirical discovery, we formulate a minimal covariant extension of General Relativity where the gravitational coupling becomes a function of the local energy-density of the continuum. This leads to a unifying cosmological relation, H²(η) = H₀² [Ωₘ η₀⁻¹ η] / [1 - η/(8π)], where η = ρ/ρ_P is a dimensionless saturation parameter. The SMC framework successfully reproduces key observational data—including Type Ia supernovae and baryon acoustic oscillations—without invoking dark matter or a cosmological constant. It makes distinct, falsifiable predictions for the Cosmic Microwave Background (e.g., a reduced lensing amplitude A_L ≈ 0.92) and the growth of large-scale structure, providing a testable alternative to the standard ΛCDM cosmological model. 10.5281/zenodo.18130993 https://orcid.org/0009-0006-5152-069X