  An ordinary differential equation describing the transverse profiles of
U-shaped glacial valleys, derived with a variational principle, has two formal
analogies which we analyze. First, an analogy with point particle mechanics
completes the description of the solutions. Second, an analogy with the
Friedmann equation of relativistic cosmology shows that the analogue of a
glacial valley profile is a universe with a future singularity but respecting
the weak energy condition. The equation unveils also a Big Freeze singularity,
which was not observed before for positive curvature index.
