Research Note

A coordinate-independent technique for detecting globally inhomogeneous flat topologies

Institute of Astronomy, School of Science, University of Tokyo, 2-21-1, Osawa, Mitaka, 181-0015 Tokyo, Japan
e-mail: hfujii@ioa.s.u-tokyo.ac.jp

Received: 8 August 2011
Accepted: 6 February 2012

Abstract

A flat Universe model that is supported by recent observations can choose among 18 possibilities 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 to make for globally inhomogeneous models because of the long time needed for the calculation. In this brief paper we provide an object-based 3D method to overcome the problem, as an extension of Fujii & Yoshii (2011, A&A, 529, A121). 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 flat Universe.