A spatial-correlation analysis of the cubic 3-torus topology based on the Planck 2013 data

TL;DR

This paper investigates the cubic 3-torus topology of the universe using Planck 2013 data, employing a spatial-correlation method to identify potential topological signatures in the CMB, and finds a promising configuration consistent with simulations.

Contribution

It introduces a spatial-correlation approach to detect multiply connected topologies in the CMB and applies it to Planck data, discovering a configuration that matches simulated topological correlations.

Findings

Identified a cubic 3-torus configuration with correlations similar to simulations.

Demonstrated the potential of spatial correlations to detect universe topology.

Highlighted the high false-positive rate of the method.

Abstract

Spatial correlations of the cubic 3-torus topology are analysed using the Planck 2013 data. The spatial-correlation method for detecting multiply connected spaces is based on the fact that positions on the cosmic microwave background (CMB) sky, that are separated by large angular distances, can be spatially much nearer according to a hypothesized topology. The comparison of the correlations computed with and without the assumed topology can reveal whether a promising topological candidate is found. The level of the expected correlations is estimated by CMB simulations of the cubic 3-torus topology and compared to those obtained from the Planck data. An interesting 3-torus configuration is discovered which possesses topological correlations of the magnitude found in the CMB simulations based on a toroidal universe. Although the spatial-correlation method has a high false-positive rate, it is striking that there exists an orientation of a cubic 3-torus cell, where correlations between points that are separated by large angular distances, mimic those of closely separated points.