A Variational Efficiency Framework for Cosmic Redshift and Spacetime Dynamics: The Master Propagation Equation as a Unified Alternative to $\Lambda$CDM Cosmology

This paper presents a variational efficiency framework governed by a single refined master propagation equation in local differential form along null geodesics. Derived from a compact action functional, the framework unifies the exponential softening of high-grade energy, void-state unfolding (volume creation), and symmetric folding in regions of concentrated energy density. It offers a classical description of spacetime dynamics and apparent cosmological expansion without requiring a global kinematic scale factor, exotic dark sector fluids, or a primordial hot dense phase.

Key theoretical and observational highlights include:

• Parsimonious Parameter Space: The framework operates on only three explicitly constrained parameters ($\tau = 14.1 \pm 1.2$ Gyr, $\delta \approx 0.08 \pm 0.03$, and $\eta_{ac}$). The acoustic exponent responsible for resonant propagation statistics is rigorously derived exactly as $\alpha = 1/7$ from the stationary-point solution of the master functional, eliminating it as a free parameter.

   

• Concordance with Modern Datasets: Utilizing mode-dependent timescales, the model achieves competitive goodness-of-fit values on the combined DESI DR2 BAO and Planck CMB data vectors. Because symmetric folding is negligible in low-density environments, the framework predicts minimal intrinsic galaxy size evolution, providing a superior fit to the unevolved angular-diameter-redshift relations observed in the JWST ASTRODEEP catalog.

   

• Geometric Resolution to the Hubble Tension: The built-in asymmetry parameter ($\delta$) naturally dictates a divergence in effective distance accumulation between void-dominated and mass-clustered lines of sight, analytically deriving distinct early ($H_{0}^{early} \approx 67.8$) and late ($H_{0}^{late} \approx 71.2$) apparent expansion rates.

   

• Strict Falsifiability in Strong-Field Gravity: The framework derives black hole thermodynamics (yielding the Bekenstein-Hawking entropy $S=A/4$) purely from the spatial degeneracy of high-grade energy driven by extreme symmetric folding. Crucially, this mechanism predicts "folding-induced damping" in gravitational-wave ringdown spectra. The paper explicitly frames this prediction against the rigorous 4% to 10% observational constraints established by the recent, high-SNR GW250114 binary black hole merger, offering a clear, testable signature for current and third-generation interferometers.