A coordinate-independent technique for detecting globally inhomogeneous flat topologies

A flat Universe model supported by recent observations has 18 possible choices for its overall topology. To detect or exclude these possibilities is one of the most important tasks in modern cosmology, but it has been very difficult for globally inhomogeneous ones because of a long-time calculation. In this brief paper we provide an object-based 3D method to overcome the problem, as an extension of Fujii & Yoshii (2011a). Though the test depends on the observer's location in the universe, this method drastically reduces calculation times to constrain inhomogeneous topologies, and will be useful in exhaustively constraining the size of the Universe.