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

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arxiv astro-ph/0501001 v1 pith:RYXW7ALK submitted 2004-12-31 astro-ph

Amir Hajian , Tarun Souradeep This is my paper · ORCID
classification astro-ph
keywords methodbipsapplicationsbipolarcosmicfastformalismhajian
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Testing Statistical Isotropy on the Sphere with Minkowski Tensors

    astro-ph.CO 2026-07 conditional novelty 7.0 of 10

    Connected-patch orientation correlations ξ±(θ,ν) give a coordinate-independent test of statistical isotropy on the sphere and separate global from local alignment in sheared random fields, while dipole modulation leav...

  2. Fr\'echet Vectors as sensitive tools for blind tests of CMB anomalies

    astro-ph.CO 2024-11 conditional novelty 5.0 of 10

    Fréchet Vectors, built from Multipole Vectors, are more sensitive to CMB anisotropies, and Planck 2018 temperature maps show small tensions with a Gaussian and statistically isotropic sky.

  3. Probing the Cosmological Principle with weak lensing shear

    astro-ph.CO 2024-11 conditional novelty 4.0 of 10

    A Euclid-like weak lensing survey could detect the E-B shear cross-correlation produced by late-time anisotropic expansion, yielding a new probe of the Cosmological Principle.

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