Spherical Orbifolds for Cosmic Topology

TL;DR

This paper introduces a novel harmonic analysis approach using orbifolds derived from Platonic spherical manifolds to improve detection of cosmic topology in the CMB radiation.

Contribution

It combines point symmetry and deck transformations to develop eigenmodes on orbifolds, advancing methods for cosmic topology analysis.

Findings

Eigenmodes expressed as linear combinations of Wigner polynomials

New tools for detecting cosmic topology from CMB data

Enhanced analysis framework for spherical orbifolds

Abstract

Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.