Orbifold Line Topology and the Cosmic Microwave Background

Abstract

We extend our study of a universe with a non-classical stringy topology, and consider an orbifold line topology, $\mathbb{R}\times\mathbb{R}^2/\mathbb{Z}_p$. This topology has a fixed line and identifies each point in space with $p-1$ other points. An observable imprint of an orbifold line on the CMB is the appearance of up to $(p-1)/2$ pairs of matching circles. Searching the WMAP data for matching circles, we can rule out an orbifold line topology with $p$ up to 10, except for $p=8$. While the significance of the peak at $p=8$ varies between data releases of WMAP, it does not appear in Planck data, enabling us to rule out $p=8$ as well.