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 topology. 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 beyond the cosmic horizon. We propose a set of measures,Kl (l = 1, 2,3,...) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. We numerically compute the predictedKl spectra for CMB anisotropy in flat torus universe models. Characteristic signatures of different models in theKl spectrum are noted.
Volume 94, 2020
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