Analogy between freezing lakes and the cosmic radiation era

Abstract

An equation describing a one-dimensional model for the freezing of lakes is shown to be formally analogous to the Friedmann equation of cosmology. The analogy is developed and used to speculate on the change between two hypothetical "spacetime phases" in the early universe.

Cosmological and thermodynamics analysis in Weyl gravity

“…For the expansion of the universe many theories have represented models, however none of them was totally fruitful. GR was not conformally invariant theory [27], therefore, as an alternative theory of GR modified conformal gravity was proposed [28,29]. Under the scale transformation the conformal Weyl gravity is the primary gravitational theory which is constant.…”

A Symmetry of the Einstein–Friedmann Equations for Spatially Flat, Perfect Fluid, Universes

“…The symmetry map (2.10)-(2.12) for the special case of a radiation fluid with equation of state parameter w = 1/3 was already noted in the context of an analogy between the cosmic radiation era and the freezing of bodies of water in environmental physics [27].…”

Lagrangian formulation of Omori’s law and analogy with the cosmic Big Rip

“…(8). The facts that the Friedmann equation looks like an energy conservation equation for one-dimensional motion and that it can describe a variety of different universes makes it suitable for several analogies between the cosmos and unrelated physical systems, including Bose-Einstein condensates [14][15][16][17][18][19], glacial valleys [20][21][22], capillary fluids [23], equilibrium beach profiles [24], and freezing bodies of water [25].…”