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  • Open Access

Freezing lakes as analog models of ΛCDM cosmology and beyond

Lorens F. Niehof*,†

Ananya Venkatasubramanian*,‡ and Federico Toschi§

Stefano Liberati∥

  • *These authors contributed equally to this work.
  • †Contact author: l.f.niehof@student.tue.nl
  • ‡Contact author: a.venkatasubramanian@student.tue.nl
  • §Contact author: f.toschi@tue.nl
  • ∥Contact author: liberati@sissa.it
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Phys. Rev. D 113, 123523 – Published 11 June, 2026

DOI: https://doi.org/10.1103/cw4j-q9ch

Abstract

We extend previous conduction-based analogies between ice growth in a lake and cosmological expansion by incorporating buoyancy-driven heat transport. Reformulating the Stefan problem with both conductive and convective fluxes yields an evolution equation for the ice thickness s(t) that is structurally analogous to the Friedmann equations for the cosmological scale factor a(t). Beyond reproducing radiation-, matter-, and curvaturelike behaviors, we introduce a reduced description of convection in which the vertically integrated heat flux reaching the moving ice-water interface is modeled as a power-law function of the instantaneous liquid-layer thickness, generating two additional effective contributions. The first is a constant term, directly analogous to a cosmological constant, arising from the persistence of buoyancy-driven transport under geometric confinement. The second is an s−1 contribution originating from the coupling between the moving ice boundary and the convective boundary layer. This term reflects the specific reduced flux-height ansatz adopted, rather than a universal physical prediction. When expressed in Friedmann-like cosmological form, this term entails a fluid with negative energy density and equation-of-state parameter w=−2/3. In cosmology this term may be an effective one associated to a network of domain walls made of exotic energy/matter, but it might also arise from an energy exchange between cosmological components. Overall, the results should be interpreted as a structural analogy between evolution equations, showing how nonlinear transport mechanisms in a classical moving-boundary problem can reproduce the hierarchy of scaling terms familiar from cosmology within a reduced and analytically tractable framework.

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Phys. Rev. D 113, 123523– Published 11 June, 2026
  • Received 26 March 2026
  • Accepted 11 May 2026
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