INVISIBILITY CLOAKING AND TRANSFORMATION OPTICS FOR THREE DIMENSIONAL MANIFOLDS AND APPLICATIONS IN COSMOLOGY.

We consider how transformation optics and invisibility cloaking can be used to construct models in subsets ℝ³ 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. Our model can be used in two ways. First, the model makes it possible to do mathematical analysis on a compact 3-manifold M by smoothly embedding the set M \ L, where L is a finite union of closed curves, to an open subset of ℝ³. Second, the model 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 (ℝ₊ x M, -dt² + g), where (M, g) is a closed, orientable, C^∞-smooth, 3- dimensional Riemannian manifold. Thus the obtained device could be used to simulate cosmological models using metamaterial devices. [ABSTRACT FROM AUTHOR]