Node-Density Field Cosmology and Galactic Dynamics: A Unified Model

We present a unified framework for cosmology and galactic dynamics grounded in a scalar node-density field ρₙ(χ,t) whose dynamics are governed by four universal organizing principles: interconnectedness, balance, feedback, and defect-free (integrity) evolution. Starting from a covariant action, we derive modified Einstein field equations that satisfy the contracted Bianchi identity by construction, a dimensionally consistent modified Friedmann equation, and a galaxy-rotation velocity formula with physically meaningful node-density corrections. The model reproduces flat galaxy rotation curves without invoking dark matter, and provides modified predictions for cosmic expansion consistent with Hubble parameter measurements and Type Ia supernova distance moduli. Fitting the two free coupling parameters α and β to observational data yields a statistically acceptable description of all three data sets. This framework offers a testable alternative to the ΛCDM dark-matter/dark-energy paradigm.