Spherical Freezing Analogy for Cosmology

Abstract: We develop a spherical freezing analogy for cosmological expansion. In the isotropic limit, a Stefan-type growth law for the ice radius gives \(R(t)\propto t^{1/2}\) and hence \(H_R^2\propto R^{-4}\), matching the scaling of a radiation-dominated Friedmann universe. We then introduce an actively cooled isothermal core, which allows freezing in a warmer water bath and provides a more controllable experimental setting. Weak anisotropy is described through a quadrupolar deformation of the interface and related to anisotropic expansion variables. Finally, phase-field AFiD-MuRPhFi simulations validate the isotropic scaling and show that strong-core freshwater convection leaves the interface nearly circular, while controlled wall-forced conduction produces a robust leading elliptic deformation.