IUCAA Preprints

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Author: search.filters.author.Hajian, AmirSubject: search.filters.subject.CMB

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    Statistical isotropy of CMB and cosmic topology
    (2011-07-05) Hajian, Amir; Souradeep, Tarun
    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 statisti- cal 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 hori- zon. We study a set of measures, κℓ (ℓ = 1, 2, 3, . . .) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. The main goal here is to interpret the κℓ spectrum and relate it to characteristic patterns in the correlation function of CMB anisotropy arising from cosmic topology. We numerically compute the predicted κℓ spectrum for CMB anisotropy in flat torus universe models. The essential features are captured in the leading order approximation to the correlation function where κℓ can be calculated analytically. The κℓ spectrum is shown to reflect the number, importance and relative orientation of principal directions in the CMB correlation dictated by the shape of the Dirichlet domain (DD) of the compact space and its size relative to cosmic horizon. Hence, besides detecting cosmic topology, κℓ can discriminate between different topology of the universe complementing ongoing search for cosmic topology in CMB anisotropy data.
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    Statistical isotropy of CMB anisotropy from WMAP
    (2005-02-01) Souradeep, Tarun; Hajian, Amir
    The statistical expectation values of the temperature fluctuations of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using bipolar spherical harmonic power spectrum proposed in Hajian & Souradeep 2003. The Bipolar Power Spectrum (BiPS) is estimated for the full sky CMB anisotropy maps of the first year WMAP data. The method allows us to isolate regions in multipole space and study each region independently. This search shows no evidence for violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to l ≈ 60 .
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    Statistical isotropy of CMB polarization maps
    (2006-06-25) Basak, Soumen; Hajian, Amir; Souradeep, Tarun
    We formulate statistical isotropy of CMB anisotropy maps in its most general form. We also present a fast and orientation independent statistical method to determine deviations from statistical isotropy in CMB polarization maps. Importance of having statistical tests of departures from SI for CMB polarization maps lies not only in interesting theoretical motivations but also in testing cleaned CMB polarization maps for observational artifacts such as residuals from polarized foreground emission. We propose a generalization of the Bipolar Power Spectrum (BiPS) to polarization maps. Application to the observed CMB polarization maps will be soon possible after the release of WMAP three year data. As a demonstration we show that for E-polarization this test can detect breakdown of statistical isotropy due to polarized synchrotron foreground.