Spherical spaces for cosmic topology and multipole selection rules

TL;DR

This paper investigates spherical manifolds as models for cosmic topology, focusing on their harmonic analysis and implications for cosmic microwave background multipole patterns, highlighting special orbifolds with unique eigenmodes.

Contribution

It introduces four specific orbifold spherical spaces with low volume fractions and distinct multipole selection rules, advancing understanding of cosmic topology models.

Findings

Orbifolds exhibit sharp multipole selection rules.

Certain spherical spaces have low volume fractions.

Analysis supports specific topological explanations for CMB observations.

Abstract

Spherical manifolds yield cosmic spaces with positive curvature. They result by closing pieces from the sphere used by Einstein for his initial cosmology. Harmonic analysis on the manifolds aims at explaining the observed low amplitudes at small multipole orders of the cosmic microwave background. We analyze assumptions of point symmetry and randomness for spherical spaces. There emerge four spaces named orbifolds, with low volume fraction from the sphere and sharp multipole selection rules in their eigenmodes.