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