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

Abstract

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 ± 0.5 km/s/Mpc) and locally measured (H₀ = 73.0 ± 1.0 km/s/Mpc) values of the Hubble constant is modeled as arising because each measurement probes the universal oscillation at a different phase angle. The dimensionless background amplitude A = 1/2 is derived as a geometric ratio from the Dirichlet boundary condition at the causal horizon; we adopt this as a normalization condition, eliminating A as a free parameter. The time-dependent energy density of the oscillating field is computed from the canonical energy-momentum tensor T₀₀, yielding a phase correction proportional to sin⁴(Φ). The nonlinear coupling constant λ = 5.09 is determined self-consistently from the two observed H₀ endpoints (H_CMB and H_local); it is O(1) and 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, distinguishable from all smooth w(z) interpolations, testable by DESI, Euclid, and the Vera C. Rubin Observatory within five years. A further consequence is that the Hubble tension is time-dependent, oscillating with period T ~ 93.0 Gyr. The sin⁴(Φ) phase dependence naturally mimics the time-evolving dark energy equation of state (w₀ > −1, w_a < 0) recently favoured by DESI DR2, and the corrected additive Friedmann equation yields CPL parameters w₀ ≈ −0.81, w_a ≈ −0.31. Comparison with DESI DR2 BAO measurements confirms radial distance predictions at all six redshift bins; the framework achieves χ² = 21.51 versus 23.05 for ΛCDM (Δχ² = −1.54) across the combined D_H/r_d and D_M/r_d observables at all six redshift bins (12 data points total; see methodological note in Section 5.7).