The Decoupling Mechanism as a Boundary Condition: Geometric Resolution to the Dark Sector and Hubble Tensions

We test whether radiative decoupling surfaces admit a scale-independent geometric normalization that can be evaluated at stellar photospheres and projected to the cosmic horizon. By coupling independently measured radiative observables with Newtonian surface gravity, we define a dimensionless boundary invariant, \mathcal{X}. Using a benchmark sample of 190 detached eclipsing-binary (DEB) components, we find that stellar photospheres cluster near the projected blackbody phase-space capacity \mathcal{X}_0 = \pi^3/15 \simeq 2.067. While evaluating this invariant using standard macroscopic relations yields an algebraic tautology, this strict circularity mathematically demonstrates that standard physical laws inherently force mass and gravity to perfectly cancel at the radiative boundary, leaving a pure geometric invariant. Projecting this identical, mass-independent boundary normalization to the Hubble horizon yields a parameter-free prediction for the dark energy density fraction, \Omega_\Lambda = \pi^3/45 \simeq 0.6890, consistent with Planck constraints. Assuming a spatially flat universe, this boundary capacity strictly mandates a total matter density fraction of \Omega_m = 1 - \pi^3/45 \simeq 0.3110, seamlessly matching empirical consensus without fine-tuning. Finally, expressing the transition from a continuous early-universe fluid to a discrete late-universe void network as a geometric packing gap, motivated by the optimal local packing limit (k=12), yields a kinematic mapping H_0^{\mathrm{local}} = H_0^{\mathrm{CMB}}(13/12) \simeq 73.0\,\mathrm{km\,s^{-1}\,Mpc^{-1}}. This geometric formulation natively resolves the most persistent cosmological anomalies through pure spatial boundaries.

Key Predictive Results

This framework introduces a parameter-free, purely geometric formulation that natively resolves three of the most persistent anomalies in modern cosmology without the need for unobserved parameters or fine-tuning:

Dark Energy (\Omega_\Lambda): Evaluated as a projected 2D horizon surface capacity rather than a 3D bulk volume density, yielding \Omega_\Lambda = \pi^3/45 \simeq 0.6890.

Total Matter (\Omega_m): Derived directly from the spatial flatness constraint (\Omega_{\mathrm{tot}}=1) as the complementary geometric remainder, yielding \Omega_m = 1 - \pi^3/45 \simeq 0.3110.

The Hubble Tension (H_0): Modeled as a kinematic offset reflecting the mandatory geometric packing gap between a continuous early-universe fluid and a discrete late-universe void network (based on the kissing number k=12), yielding H_0^{\mathrm{local}} = H_0^{\mathrm{CMB}}(13/12) \simeq 73.0 \mathrm{km\,s^{-1}\,Mpc^{-1}}.

Repository Contents

Manuscript.pdf: The full research paper.

verify_boundary.py: A self-contained, reproducible Python script that performs the empirical validations and computes the cosmological projections.

data.csv: The empirical benchmark dataset of 190 detached eclipsing binary (DEB) components from Torres et al. (2010) used for the photospheric evaluation.