A Phase-Dependent Mechanism for the Hubble Tension from Oscillatory Spacetime- Framework

We propose a mechanism for the Hubble tension in which spacetime is modelled as a self-oscillating scalar field in a non-zero ground state. The 8.3% discrepancy between CMB-inferred H0 = 67.4 km/s/Mpc and locally measured H0 = 73.0 km/s/Mpc is modelled as arising because each measurement probes the universal oscillation at a different phase angle. The background amplitude A = 1/2 is established as a geometric normalization choice from the Dirichlet boundary condition at the causal horizon, eliminating it as a free parameter. Because the exact damped cosmological field equation is intractable, we derive the oscillatory correction from the structural symmetries of the canonical energy-momentum tensor T00 combined with the cosmological Virial theorem, yielding a unique phase correction proportional to sin⁴(Φ).

The nonlinear coupling constant is determined self-consistently from the two observed H0 endpoints; it satisfies naturalness, but is not an independent prediction—it encodes the amplitude of the Hubble tension. The predictive content of the framework lies in the functional form of H(z): the sin⁴(Φ) phase profile at intermediate redshifts is distinguishable from all smooth w(z) interpolations. A full-covariance statistical analysis against DESI DR2 BAO measurements (incorporating the official DM/DH anti-correlations) yields a Δχ² = −8.47 improvement over flat ΛCDM across the primary 10-bin sample. The phase dependence additionally produces an effective phantom dark energy equation of state (w0 = −1.186), consistent with the framework's bimetric class membership.

About This Repository

This record serves as the complete, reproducible archival package for the oscillatory spacetime framework. It contains the primary manuscript, theoretical companion papers, step-by-step mathematical derivations, and the Python code required to reproduce all tables, figures, and statistical claims from the text.

Input vs. Prediction

To evaluate this framework, readers should note the structural distinction between inputs and predictions:

• Inputs: The early-universe (H_CMB) and late-universe (H_local) expansion rates are inputs. They are used as boundary conditions to fix the phase and coupling constant. The framework does not predict these endpoints from first principles.

• Predictions: The genuine, falsifiable predictions of this theory are the intermediate-redshift H(z) curve shape, the phantom dark energy equation of state (w(z) < −1), and the improved fit to intermediate BAO observables.

Definitive Statistical Baseline

The definitive statistical benchmark for this framework is the full-covariance DESI DR2 analysis (detailed in Section 5.4 and computed via the attached full_cov_chisq1.py script), which demonstrates that the framework's specific DM/DH signature aligns significantly better with the correlated DESI measurements than ΛCDM.

File Inventory

• Main Manuscript (Hubble-Tension-final.docx): The primary paper detailing the mechanism, the self-consistent Friedmann integration, the DESI DR2 full-covariance comparison, and the unbroken derivation chain from the Bekenstein disformal metric to the sin⁴(Φ) correction.

• Companion Paper (Vacuum-Energy-final.docx): Demonstrates how the oscillatory spacetime framework's bounded-domain geometry reduces the standard QFT vacuum catastrophe, leaving a decomposable residual factor of ~17 without invoking UV mode summation.

• Quantum Foundations Paper (Quantum-Scalar-Foundations-final.docx): Establishes the bounded-domain QFT foundations of the oscillatory spacetime framework, deriving the scalar field mass and the quantum stability parameter δ_Q.

• Supplementary Note (Supplementary-Variational-Note-final.docx): The explicit, step-by-step variational derivation of the master field equations, including the structural derivation of the sin⁴(Φ) correction via the Z₂-symmetric quartic self-interaction and the cosmological Virial theorem (Turner 1983).

• Technical Note (Duffing-Technical-Note-final.docx): Solves the exact un-damped Duffing oscillator using Jacobi elliptic functions to rigorously prove that the oscillatory spacetime framework's quantitative conclusions are robust against the sinusoidal approximation.

• Holographic Proof (Holographic-Proof-final.docx): Auxiliary theoretical note demonstrating equivalence with holographic dark energy scaling laws.

• Quantum Entanglement Paper (OSF-Entanglement-final.docx): Derives the vacuum entanglement structure of the oscillatory spacetime framework, including the Unruh-DeWitt detector concurrence, the position anisotropy result, and Bell-CHSH analysis.

• Entanglement Derivation (OSF-Entanglement-Derivation-final.docx): Step-by-step mathematical derivation of the two-point Wightman function for the framework field on the Dirichlet domain, the closed-form concurrence formula, and the full multi-mode position anisotropy calculation.

• supplementary_integration_v3.py: Python script that performs the self-consistent Friedmann integration. Reproduces all data tables across the main and companion manuscripts.

• full_cov_chisq1.py: Python script that computes the DESI DR2 full-covariance χ² comparison.

To run full_cov_chisq1.py, first create a desi_dr2/ subfolder in the same directory and download two files from the CobayaSampler GitHub repository (desi_gaussian_bao_ALL_GCcomb_mean.txt and desi_gaussian_bao_ALL_GCcomb_cov.txt). Then run python3 full_cov_chisq1.py.

Expected output for the primary 10-bin sample: Framework χ² = 18.22, ΛCDM χ² = 26.69, Δχ² = −8.47.