Freezing lakes as analogue models of $Λ$CDM cosmology and beyond
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866908887298342912 |
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| author | Niehof, Lorens F. Venkatasubramanian, Ananya Toschi, Federico Liberati, Stefano |
| author_facet | Niehof, Lorens F. Venkatasubramanian, Ananya Toschi, Federico Liberati, Stefano |
| contents | 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 curvature-like 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 a $s^{-1}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_24019 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Freezing lakes as analogue models of $Λ$CDM cosmology and beyond Niehof, Lorens F. Venkatasubramanian, Ananya Toschi, Federico Liberati, Stefano General Relativity and Quantum Cosmology 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 curvature-like 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 a $s^{-1}$ 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. |
| title | Freezing lakes as analogue models of $Λ$CDM cosmology and beyond |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2602.24019 |