The Dense-Vacuum Analogy: A Phenomenological Toy Model for Confinement-Type Structure Stabilisation and Its Explicit Limits

We present the Dense-Vacuum Analogy (DVA), a non-dimensional toy model that explores whether a postulated confining background medium can produce galaxy-like hydrostatic stability and, at the level of pure kinematics, an accelerating background expansion of the same functional form as the CPL w0, wa parametrisation already used in mainstream dark-energy phenomenology. We state this model's assumptions as explicit postulates rather than derived results, and we are explicit about what the model does not do: it does not derive, and does not claim to derive, any quantitative relationship between the confinement density scale required for galactic-scale stability and the cosmological vacuum energy density inferred from cosmic microwave background and large-scale-structure data. That relationship, structurally identical to the cosmological constant problem, remains an explicitly open, unresolved gap in this framework (see the Model Postulates section, Postulate P3, and the Limitations section). Within this declared scope, we provide: (i) a numerically verified linear stability (Jeans-type) analysis showing that the postulated confinement mechanism suppresses gravitational collapse across the sampled wavenumber range in a controlled toy setting; (ii) a reproducible N-body toy simulation of the postulated pairwise confinement force, with a full variance-based (Sobol/Saltelli) global sensitivity analysis; (iii) explicit, falsifiable predictions tied to existing observational techniques (stacked weak-lensing measurements around cosmic voids); and (iv) a roadmap identifying the specific theoretical work required before this toy model could be upgraded to a candidate physical theory. All numerical results are produced by the self-contained Python script reproduced in Appendix B and are internal consistency checks of the stated equations; none constitute a fit to, or an empirical claim about, real astronomical survey data.