A coordinate-independent technique for detecting globally inhomogeneous flat topologies

TL;DR

This paper introduces a new 3D object-based method to efficiently detect or exclude inhomogeneous flat topologies of the universe, significantly reducing computational effort in cosmological topology analysis.

Contribution

It extends previous methods to handle globally inhomogeneous topologies, enabling faster and more comprehensive constraints on the universe's shape.

Findings

Reduces calculation times for topology detection

Enables exhaustive constraints on universe size

Applicable to inhomogeneous flat topologies

Abstract

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.