IUCAA Preprints
Permanent URI for this communityhttp://localhost:4000/handle/11007/149
Browse
7 results
Search Results
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 Statistical isotropy of CMB and cosmic topology(2011-07-05) Hajian, Amir; Souradeep, TarunThe 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.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.Item Statistical isotropy of CMB anisotropy from WMAP(2005-02-01) Souradeep, Tarun; Hajian, AmirThe 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 .Item Statistical isotropy of CMB polarization maps(2006-06-25) Basak, Soumen; Hajian, Amir; Souradeep, TarunWe 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.Item Cosmic microwave background bipolar power spectrum: Basic formalism and applications(2005-01-01) Hajian, Amir; Souradeep, TarunWe study the statistical isotropy (SI) of temperature fluctuations of the CMB as dis- tinct from Gaussianity. We present a detailed formalism of the bipolar power spectrum BiPS) which was introduced as a fast method of measuring the statistical isotropy by Hajian & Souradeep 2003. The method exploits the existence of patterns in the real space correlations of the CMB temperature field. We discuss the applications of BiPS in constraining the topology of the universe and other theoretical scenarios of SI violation. Unlike the traditional methods of search for cosmic topology, this method is computationally fast. We also show that BiPS is potentially a good tool to detect the effect of observational artifacts in a CMB map such as non-circular beam, anisotropic noise, etc. Our method has been successfully applied to the Wilkinson Microwave Anisotropy Probe sky maps by Hajian et al. 2004, but no strong evidence of SI violation was found.Item Measuring statistical isotropy of CMB anisotropy(2006-07-25) Souradeep, Tarun; Hajian, Amir; Basak, SoumenThe statistical expectation values of the temperature fluctuations and polarization of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy (SI) of the CMB maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using the bipolar spherical harmonic formalism proposed in Hajian & Souradeep 2003 for CMB temperature anisotropy and extended to CMB polarization in Basak, Hajian & Souradeep 2006. The Bipolar Power Spectrum (BiPS) had been measured for the full sky CMB anisotropy maps of the first year WMAP data and now for the recently released three years of WMAP data. We also introduce and measure directional sensitive reduced Bipolar coefficients on the three year WMAP ILC map. Consistent with our published results from first year WMAP data we have no evidence for violation of statistical isotropy on large angular scales. Preliminary analysis of the recently released firstWMAP polarization maps, however, indicate significant viola- tion of SI even when the foreground contaminated regions are masked out. Further work is required to confirm a possible cosmic origin and rule out the (more likely) origin in observational artifact such as foreground residuals at high galactic latitude.