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We consider how transformation optics and invisibility cloaking can be usedto construct models in subsets $\mathbb{R}^3$ with a varying metric, where thetime-harmonic waves for a given angular wavenumber $k$, are equivalent to thewaves in some closed orientable manifold. The obtained models could inprinciple be physically implemented using a device built from metamaterials. Inparticular the measurements in the metamaterial device given by the Helmholtzsource-to-solution operator are equivalent to Helmholtz source-to-solutionmeasurements in a universe given by $(\mathbb{R}_+\times M, -dt^2 +g)$, where$(M,g)$ is a closed, orientable, $C^\infty$-smooth, 3-dimensional Riemannianmanifold. Thus the obtained construction could be used to simulate cosmologicalmodels using metamaterial devices.

Transformation Optics for the Modelling of Waves in a Universe with Nontrivial Topology