The no-defect conjecture in cosmic crystallography

TL;DR

This paper reviews the potential presence of topological defects in multi-connected cosmic spaces and concludes they are either unlikely to form or space appears simply connected on observable scales.

Contribution

It explores the implications of space topology on defect formation, providing insights into cosmic topology and defect likelihood.

Findings

Topological defects are unlikely to form in multi-connected spaces.

Space is effectively simply connected on scales up to the horizon.

The formation of defects depends on the topology of the universe.

Abstract

The topology of space is usually assumed simply connected, but could be multi-connected. We review in the latter case the possibility that topological defects arising at high energy phase transitions might still be present and find that either they are very unlikely to form at all, or space is effectively simply connected on scales up to the horizon size.