  This article shows that the compactified Milne universe geometry, a toy model
for the big crunch/big bang transition, can be realized in hyperbolic
metamaterials, a new class of nanoengineered systems which have recently found
its way as an experimental playground for cosmological ideas. On one side,
Klein-Gordon particles, as well as tachyons, are used as probes of the Milne
geometry. On the other side, the propagation of light in two versions of a
liquid crystal-based metamaterial provides the analogy. It is shown that ray
and wave optics in the metamaterial mimic, respectively, the classical
trajectories and wave function propagation, of the Milne probes, leading to the
exciting perspective of realizing experimental tests of particle tunneling
through the cosmic singularity, for instance.
