A Geometric Foam Model for the Cosmological Constant, Newton's Constant, and Dark Matter Halos

Abstract In plain language: This paper proposes that the universe behaves like a soap-bubble surface with swirling vortices underneath, and shows how this simple picture can explain gravity, quantum mechanics, dark matter, and the universe's expansion—with testable predictions for experiments in the next 5 years. I propose a unified hydrodynamic framework in which gravity, quantum mechanics, and cosmology emerge from a single physical substrate: a dynamically active foam interface endowed with surface tension and coupled bulk vortex flows. In this Rozier Foam Model, spacetime is the interface; curvature corresponds to surface tension gradients; and matter/fields arise as coherent excitations supported by underlying vorticity and capillary dynamics.In the macroscopic limit, gravitational dynamics follow from the Young–Laplace–like balance on the interface, yielding the Einstein equations and standard tests of general relativity when surface tension responds locally to energy–momentum. At mesoscopic scales, pilot-wave hydrodynamics on the interface reproduces quantum phenomena—interference, tunneling, and nonlocal entanglement—via guiding surface modes coupled to sub-interface circulation. Galactic and cluster-scale “dark matter” effects are explained by quantized vortex circulation in the bulk, predicting flat rotation curves, weak-lensing convergence, and dynamical stability without cold collision less particles. The cosmological constant emerges as a global curvature of the foam, Λ = H₀²/c², linking vacuum energy to the Hubble parameter. Black hole thermodynamics arises from horizon surface dynamics: capillary-mode emission reproduces Hawking spectra while information is preserved in correlated interfacial phase and vortex degrees of freedom.The model makes falsifiable predictions: mild frequency-dependent gravitational-wave dispersion and horizon echoes; no primordial tensor modes (r < 10⁻⁴); femto- to micro-lensing from vortex cores; a modified late-time ISW effect; and a sharp sub halo mass cutoff set by vortex quantization. Connections to superfluid helium, analog gravity, and pilot-wave experiments provide laboratory access to key mechanisms and parameters. Together, these results outline a testable alternative to ΛCDM+GR+QFT and a concrete experimental roadmap—combining astrophysical surveys, gravitational-wave spectroscopy, and table-top hydrodynamics—to confirm or refute the foam paradigm within the next decade