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We reformulate the variational problem describing equilibrium beach profiles in the thermodynamic approach of Jenkins and Inman [J. Geophys. Res.: Oceans 111, C02003 (2006)10.1029/2005JC002899]. A first integral of the resulting Euler-Lagrange equation coincides formally with the Friedmann equation ruling closed universes in relativistic cosmology, leading to a useful analogy. Using the machinery of Friedmann-Lemaître-Robertson-Walker cosmology, qualitative properties and analytic solutions of beach profiles, which are the subject of a controversy, are elucidated.