Light propagation through random hyperbolic media: from a pile of sand to large scale structure of present day universe

We analyze electromagnetic field propagation through a random medium which consists of hyperbolic metamaterial domains separated by regions of normal "elliptic" space. This situation may occur in a problem as common as 9 micrometer light propagation through a pile of sand, or as exotic as electromagnetic field behavior in the early universe immediately after the electro-weak phase transition. We demonstrate that spatial field distributions in random hyperbolic and random "elliptic" media look strikingly different. This effect may potentially be used to evaluate the magnitude of magnetic fields which existed in the early universe.