CMB radiation in an inhomogeneous spherical space

TL;DR

This paper investigates how the topology and observer position in inhomogeneous spherical spaces affect the Cosmic Microwave Background (CMB) anisotropies, providing new insights into the relationship between space topology and CMB observations.

Contribution

It demonstrates the observer-dependent properties of CMB in inhomogeneous spherical spaces and establishes the equivalence between lens spaces and Platonic cubic spaces for harmonic analysis.

Findings

CMB anisotropies are suppressed on large scales depending on observer position.

The equivalence between lens spaces and Platonic cubic spaces is shown.

General sum rules for invariant polynomials on the 3-sphere are derived.

Abstract

We analyse the CMB radiation in spherical 3-spaces with non-trivial topology. The focus is put on an inhomogeneous space which possesses observer dependent CMB properties. The suppression of the CMB anisotropies on large angular scales is analysed with respect to the position of the CMB observer. The equivalence of a lens space with a Platonic cubic space is shown and used for the harmonic analysis. We give the transformation of the CMB multipole radiation amplitude as a function of the position of the observer. General sum rules are obtained in terms of the squares of the expansion coefficients for invariant polynomials on the 3-sphere.