Cosmic microwave background radiation in an inhomogeneous spherical space

Abstract

We analyse the cosmic microwave background (CMB) radiation in spherical three-spaces with nontrivial topology. The focus is 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 to 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 three-sphere. © 2011 The Royal Swedish Academy of Sciences.