Analogues of glacial valley profiles in particle mechanics and in cosmology

Valleys carved by glaciers are U-shaped. The theoretical modelling of glacial valley cross-sectional profiles is based on a mathematical equation which must be satisfied by these profiles. Surprisingly other, very different, physical systems satisfy the same equation. This fact leads to analogies between glacial valley transverse profiles and these other systems, bridging completely different disciplines.

Here we study two analogies. The first one is the analogy between a glacial valley profile and a classical point particle moving in one dimension under a special force. The second analogy is between glacial valley profiles and the dynamics of the universe, as modelled by general-relativistic cosmology and with an exotic fluid as its matter content. We stress that we study the analogy with possible theoretical models of the future universe dominated by an exotic dark energy, which abound in the literature, and not the actual universe at the present time which is, indeed dominated by dark energy but contains also a non-negligible proportion of dark matter. Other details of the present universe cannot be reproduced by a single equation in the analogy with glacial valley profiles.

Two advances in knowledge originate from this study. The mechanical analogy reveals a set of solutions for glacial valley transverse profiles which was missed in glaciology. A graphical qualitative method of analysis, which is standard textbook material in mechanics, allows one to classify quickly and comprehensively the qualitative solutions of the equation ruling these profiles.

The second analogy studied uncovers two interesting types of spacetime singularity (one of which dubbed “Big Freeze” singularity) which appeared recently in the cosmological literature and are generalized here. In addition to these results, it is very interesting to draw a parallel between glacial valley profiles and their cosmological counterparts, which are special universes containing exotic fluids. These fluids have been the subject of extensive literature in cosmology during the past decade. We highlight the fact that the model of glacial valley transverse profiles requires improvements, which will likely lead to new analogies.

Read the full paper — Analogues of glacial valley profiles in particle mechanics and in cosmology by Valerio Faraoni and Adriana M. Cardini on the FACETS website.

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