A Functional Interpretation of Gravitational Inaccessibility: The Hypothesis of Vibrational Wave Dispersion (HDOV)

This work presents a revised and expanded version of the Hypothesis of Vibrational Wave Dispersion (HDOV), focused on the formulation of its minimal gravitational sector as a covariant effective theory. The core of the model is organized around a projective wave equation for the scalar field Psi, a WKB transport law for the amplitude, and a leading geometric closure eta_p = xi R. In this version, this closure is explicitly formulated as a leading covariant ansatz within an EFT truncation in curvature, not as a complete microscopic derivation. As a result, functional accessibility is no longer treated as a free parametrization, but becomes dependent on the scalar curvature of the background in the regime considered.

On this basis, a minimal metric action with coupling lambda R X is derived, leading to the scalar equation, the effective field equations, the trace relation, and the reduction to a homogeneous FLRW background. Version 6 also develops the relation between the lambda R X operator and scalar-tensor theories in the formal neighborhood of Horndeski, while making clear that the truncation used here is not a complete Horndeski completion. The manuscript further introduces the minimal cosmological extension with matter and radiation, which is required to move from an idealized scalar branch to a self-consistent dynamical validation.

In the weak-field regime, the manuscript strengthens the linear limit and the post-Newtonian analysis of the minimal truncation. In the local vacuum branch with Psi_bar = 0, the scalar field is not sourced by ordinary matter at first order and the model reproduces the leading behavior of General Relativity, with gamma = beta = 1. For slowly varying homogeneous backgrounds, the dominant effect is a renormalization of G_eff without gravitational slip at linear order. Version 6 more clearly delimits the scope of this result: it is not a global PPN proof of all HDOV branches, but a compatible branch under explicit assumptions.

The comparison with Type Ia Supernovae and BAO is retained as a reproducible phenomenological benchmark. The figures, residuals and diagnostic metrics show that, within the parametric pipeline used here, the phenomenological HDOV-compatible branch may exhibit lower residuals and more favorable AIC/BIC values than a reference Lambda-CDM model implemented in the same scheme. However, Version 6 clarifies that this reading does not replace a self-consistent integration of the extended FLRW system and does not yet constitute a definitive cosmological model selection. A strong claim about cosmic acceleration without explicit dark energy would require dynamically solving the system with matter and radiation, obtaining H(z), computing SN Ia, BAO and H(z) observables, including full covariances, and verifying the EFT and stability conditions throughout the fitted range.

Overall, HDOV is presented here as a self-contained, falsifiable and mathematically more closed formulation of functional gravitational inaccessibility. Version 6 does not claim that dark energy has been ruled out or that Lambda-CDM has been replaced; rather, it establishes an effective and reproducible basis for investigating whether a geometric-functional modulation of the gravitational sector can reproduce cosmological observables without introducing an explicit dark-energy term in the regime considered.