Technical Abstract — HDC–CBC / ΩCt (Dynamical tensorial coherence, modified gravitational propagation and Hubble parameter tension) The ΩCt volume develops the dynamical tensorial extension of the HDC–CBC framework, formulating an effective realization of correlational coherence in the gravitational-wave sector and its observable cosmological impact. Unlike the Ω volume, focused on late-time activation of the background and scalar perturbations, ΩCt introduces a coherent tensorial dynamics dependent on the correlational state , preserving general relativity as a local and early-time limit, while allowing a late-time modulation of gravitational propagation without altering the electromagnetic structure of the background. The formalism is based on the quantum–geometric correlational disequilibrium principle applied to the tensor sector, where effective geometric projection induces a modified friction term and an effective tensor mass dependent on the dynamical correlational state. The resulting propagation equation preserves its second-order character and local effective covariance, but incorporates a damping function and a term that activate exclusively in the late-time regime, under hierarchical coherence conditions. This activation does not modify the luminal speed of gravitational waves nor introduce additional degrees of freedom, maintaining compatibility with constraints imposed by GW170817. A direct consequence of the framework is the emergence of an effective gravitational luminosity distance distinct from the electromagnetic one , related through an exponential factor governed by the cumulative integration of correlational tensorial dynamics. This deviation arises only at low redshifts and does not affect the acoustic horizon, recombination, or primordial physics. In this context, the observational discrepancy in the Hubble parameter can be reinterpreted as a late-time manifestation of tensorial coherence, without modifying the electromagnetic background history or introducing additional dark energy components. ΩCt systematically analyzes the conditions for dynamical stability, absence of ghost instabilities, and consistency of structure growth under a strictly late-time tensorial activation. Explicit criteria are established for continuity toward the ΛCDM limit, preservation of the basal correlational rigidity regime, and coherence between the tensor sector, background expansion, and multimessenger observables. The framework identifies regions of correlational space in which the H₀ tension can be redistributed between gravitational and electromagnetic distances without generating inconsistencies in CMB, BAO, weak lensing, or standard sirens. Overall, HDC–CBCₜ / ΩCt constitutes a conservative and operational extension of the correlational framework, in which the tensor sector acts as a dynamical channel for the late-time realization of the global vacuum equilibrium. The volume establishes the formal basis for numerical implementation and direct confrontation with multimessenger data, coherently integrating expansion, gravitational propagation, and observational consistency within a hierarchical and falsifiable scheme. The correlational coherence is endowed with a minimal effective dynamics, transforming Ωcₜ into a closed dynamical framework rather than a purely parametric extension. In its current implementation, ΩCt/N should be understood as a minimal experimental realization of the correlational closure, based on lite observational validation, structural proxies, and calibrated effective closures. In particular, the present confrontation does not yet constitute a full Boltzmann integration or an exhaustive historical reconstruction of , but rather an operational framework for structural consistency and initial parametric falsifiability.
Jordi Audet Palau (2026) studied this question.