Saturation Dynamics and Grid Resonance: A Phenomenological Alternative to Dark Matter and Dark Energy

Abstract

We present Tolog-Alpha, a phenomenological framework based on a 3×3 stabilizing grid (Curvature, Energy Density, Scalar Field) that aims to reproduce galactic rotation curves, cosmic expansion, and baryon acoustic oscillations without invoking non-baryonic dark matter or a cosmological constant. The model introduces a redshift-dependent saturation function S(z), leading to an effective equation of state w(z) = -λ S(z), which transitions from matter-like behavior at high redshift to negative pressure at late times. We demonstrate consistency with SPARC rotation curves, Pantheon supernova data, and BAO constraints at the phenomenological level. Remaining challenges include reproducing the full CMB power spectrum, motivating a dual-phase extension of the model. Tolog-Alpha provides a testable alternative framework to ΛCDM and highlights the potential role of geometric stabilization mechanisms in cosmology.

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