A Unified Description from the Planck Scale to Dark Energy: An Energy-Efficiency Theory Synthesis

We derive a unified description of physics from the Planck scale to dark energy within Energy-Efficiency Theory (EET). Starting from the three axioms and the entropy decomposition \(S = S_c + S_f - S_{\text{corr}}\), we obtain a single dynamical equation for the constrained-state energy fraction \(f_c\). The equation is covariant under diffeomorphisms and reduces to Einstein's field equations in the macroscopic limit. It naturally reproduces quantum fluctuations at the Planck scale, classical spacetime geometry, and dark energy dominance. The framework quantitatively recovers the Hubble constant, CMB power spectrum, BAO scale, Mercury perihelion precession, gravitational lensing, and galaxy rotation curves, without invoking dark matter particles or a cosmological constant. It resolves the core–cusp, missing satellites, and too-big-to-fail problems of \(\Lambda\)CDM, and yields testable predictions with explicit statistical criteria.