Statistical isotropy of the cosmic microwave background

Abstract

The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra large scale structure of the cosmos, in particular, of non trivial cosmic topol- ogy. The statistical isotropy (SI) of the Cosmic Microwave Background temperature fluctuations (CMB anisotropy) is sensitive to this breakdown on the largest scales comparable to, and even be- yond the cosmic horizon. We propose a set of measures, κℓ (ℓ = 1, 2, 3, . . .) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. We numerically compute the predicted κℓ spectra for CMB anisotropy in flat torus universe models. Characteristic signature of different models in the κℓ spectrum are noted.