IUCAA Preprints
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Item Statistical isotropy of the cosmic microwave background(2011-07-05) Souradeep, Tarun; Hajian, AmirThe 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.Item Measuring statistical isotropy of the CMB anisotropy(2003-07-05) Ajian, Amir; Souradeep, TarunThe statistical expectation values of the temperature fluctuations of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. This assumption of statistical isotropy (SI) of the CMB anisotropy should be observationally verified since detection of violation of SI could have profound implications for cosmology. We propose a set of measures, κℓ (ℓ = 1, 2, 3, . . .) for detecting violation of statistical isotropy in an observed CMB anisotropy sky map indicated by non zero κℓ. We define an estimator for the κℓ spectrum and ana- lytically compute its cosmic bias and cosmic variance. The results match those obtained by measuring κℓ using simulated sky maps. Non-zero (bias corrected) κℓ larger than the SI cosmic variance will imply violation of SI. The SI mea- sure proposed in this paper is an appropriate statistics to investigate preliminary indication of SI violation in the recently released WMAP data.Item Statistical Isotropy of the WMAP Data: A bipolar power spectrum analysis(2011-07-06) Hajian, Amir; Souradeep, Tarun; Neil, CornishABSTRACT The statistical expectation values of the temperature fluctuations of the cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We use the bipolar power s pectrum (BiPS) proposed in Hajian & Souradeep to investigate the statistical isotropy (SI) of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP). The method can isolate and probe specific regions of choice in multipole space using appropriate window functions. The BiPS is estimated for full sky CMB anisotropy maps based on the first year WMAP data using a range of window functions. The BiPS spectra computed for both full sky maps for all our window functions are consistent with zero, roughly within 2 σ. The null BiPS results may be interpreted as an absence of strong violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to l ∼ 60. However, pending a careful direct comparison, our results do not necessarily conflict with the specific SI related anomalies reported using other statistical tests.