PHASE-DEPENDENT MECHANISM FOR THE HUBBLE TENSION: Oscillatory spacetime, exact Duffing solution, and confrontation with the Theory of Objectivity

This article offers a critical–propositional examination of Lorne Velasquez’s 2026 oscillatory-spacetime framework for the Hubble tension, now expanded through the inclusion of the supplementary Duffing analysis based on the exact Jacobi-elliptic solution. The study investigates the extent to which a phase-dependent cosmological mechanism can account for the discrepancy between CMB-inferred and locally measured values of the Hubble constant, while also testing the internal robustness of the model after the nonlinear correction of its original sinusoidal approximation. The paper argues that the Duffing supplement strengthens the proposal methodologically by showing that its central observational profile remains substantially stable even when the harmonic waveform is replaced by the exact nonlinear solution and the coupling is reconverged. At the same time, the article maintains that the framework remains ontologically derivative when confronted with the Theory of Objectivity (TO): it may be fruitful as a late-universe phenomenological model, but it does not provide a foundational account of cosmological genesis, modal necessity, or the emergence of relational structure. In dialogue with the foundational, recent, and support bibliographies of the Theory of Objectivity, the article develops a structured comparison between Velasquez’s oscillatory cosmology and TO’s modal axioms, phenomenic elements, Inductive Effects, cosmological Eras, and cosmogonic theorem. It proposes that the main value of the oscillatory-spacetime model lies not in replacing TO’s ontological framework, but in suggesting that observable cosmic expansion may preserve periodic relational modulations that can be reinterpreted, in TO terms, as phenomenic and inductive manifestations of a deeper cosmological order. The article concludes that Velasquez’s proposal deserves serious consideration as a mathematically refined and testable late-time cosmological hypothesis, while also showing that its ultimate explanatory horizon remains limited unless subordinated to a more radical modal ontology. Keywords Theory of Objectivity; Hubble tension; oscillatory spacetime; Duffing oscillator; Jacobi elliptic functions; dynamical dark energy; modal ontology; phenomenic elements; Inductive Effects; cosmogonic theorem; cosmology; phase-dependent expansion.