The Cosmic Microwave Background Bipolar Power Spectrum: Basic Formalism and Applications

We study the statistical isotropy (SI) of temperature fluctuations of the CMB as distinct 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.