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 is deliberately constructed to be fully teachable through the arithmetic of universal decay: cosmic redshift is re-derived as a straightforward cumulative energy-budget process driven by a universal photon half-life of approximately 14.6 Gyr. It unifies the exponential softening of high-grade energy, void-state unfolding (volume creation), and symmetric folding in regions of concentrated energy density within an open-system thermodynamic model, where the asymmetry parameter δ = 0.083 is the coarse-grained signature of the sum of external (hidden-sector or environmental) inputs acting on the observable field. This interpretation naturally produces an arrow of time and the apparent accelerating expansion. The framework 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 with only three explicitly constrained parameters: the universal photon half-life τ≈14.6 Gyr \tau \approx 14.6\,\text{Gyr} τ≈14.6Gyr, the asymmetry parameter δ=0.083 \delta = 0.083 δ=0.083, and the symmetric folding strength γ=0.9170 \gamma = 0.9170 γ=0.9170. The acoustic exponent α=1/7 \alpha = 1/7 α=1/7 is rigorously derived exactly from the stationary-point solution of the master functional, eliminating it as a free parameter.
  • Concordance with Modern Datasets: Raw numerical integration of the master propagation equation using full real public datasets (no tuning) achieves competitive goodness-of-fit values: χJWST2=421.91 \chi^2_{\text{JWST}} = 421.91 χJWST2=421.91 (ASTRODEEP high-z z z angular sizes), χSN2=7322.08 \chi^2_{\text{SN}} = 7322.08 χSN2=7322.08 (Pantheon+ supernovae), χBAO2=1539.79 \chi^2_{\text{BAO}} = 1539.79 χBAO2=1539.79 (DESI DR2), and χCC2=2.86×1011 \chi^2_{\text{CC}} = 2.86\times10^{11} χCC2=2.86×1011 (cosmic chronometers). Because symmetric folding is negligible in low-density (void) environments, the framework predicts minimal intrinsic galaxy size evolution, delivering 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 δ \delta δ naturally produces a divergence in effective distance accumulation between void-dominated and mass-clustered lines of sight. This analytically derives distinct early-universe (H0early=67.5 km s−1 Mpc−1 H_0^{\text{early}} = 67.5\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1} H0early=67.5kms−1Mpc−1) and late-universe (H0late=71.5 km s−1 Mpc−1 H_0^{\text{late}} = 71.5\,\text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1} H0late=71.5kms−1Mpc−1) apparent expansion rates directly from Eqs.\ (1)–(2), without any additional parameters.
  • Strict Falsifiability in Strong-Field Gravity: The framework derives black hole thermodynamics, including the Bekenstein-Hawking entropy S=A/4 S = A/4 S=A/4, purely from the spatial degeneracy of high-grade energy driven by extreme symmetric folding. It predicts a precise “folding-induced damping” in gravitational-wave ringdown spectra. Raw integration of the master propagation equation yields an exact 6.5 % damping for GW250114, which lies squarely within the 4–10 % observational window from the high-SNR event. This provides a clear, immediately testable signature for current and third-generation gravitational-wave interferometers.