Local patch analysis for testing statistical isotropy of the Planck convergence map

Abstract

The small but measurable effect of weak gravitational lensing on the cosmic microwave background radiation provide information about the large-scale distribution of matter in the universe. We use the all sky distribution of matter, as represented by the {\em convergence map} that is inferred from CMB lensing measurement by Planck survey, to test the fundamental assumption of Statistical Isotropy (SI) of the universe. For the analysis we use the $\alpha$ statistic that is devised from the contour Minkowski tensor, a tensorial generalization of the scalar Minkowski functional, the contour length. In essence, the $\alpha$ statistic captures the ellipticity of isofield contours at any chosen threshold value of a smooth random field and provides a measure of anisotropy. The SI of the observed convergence map is tested against the suite of realistic simulations of the convergence map provided by the Planck collaboration. We first carry out a global analysis using the full sky data after applying the galactic and point sources mask. We find that the observed data is consistent with SI. Further we carry out a local search for departure from SI in small patches of the sky using $\alpha$. This analysis reveals several sky patches which exhibit deviations from simulations with statistical significance higher than 95\% confidence level (CL). Our analysis indicates that the source of the anomalous behaviour of most of the outlier patches is inaccurate estimation of noise. We identify two outlier patches which exhibit anomalous behaviour originating from departure from SI at higher than 95\% CL. Most of the anomalous patches are found to be located roughly along the ecliptic plane or in proximity to the ecliptic poles.

arXiv comment23 pages, 6 figures

References in corpus (43)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Efficient Computation of CMB anisotropies in closed FRW models
• Weak Gravitational Lensing of the CMB
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• Planck 2018 results. VIII. Gravitational lensing
• Mass Reconstruction with CMB Polarization
• Gravitational Lensing Effect on Cosmic Microwave Background Polarization
• CMB Lensing Reconstruction on the Full Sky
• Planck 2015 results. XVI. Isotropy and statistics of the CMB
• Planck 2018 results. III. High Frequency Instrument data processing and frequency maps
• Detection of Gravitational Lensing in the Cosmic Microwave Background
• Reconstruction of lensing from the cosmic microwave background polarization
• CMB Anomalies after Planck
• Correlation of CMB with large-scale structure: I. ISW Tomography and Cosmological Implications
• GRAVITATIONAL LENSING EFFECT ON COSMIC MICROWAVE BACKGROUND ANISOTROPIES: A POWER SPECTRUM APPROACH
• Minkowski Functionals used in the Morphological Analysis of Cosmic Microwave Background Anisotropy Maps
• The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity
• High redshift radio galaxies and divergence from the CMB dipole
• Probing the Cosmological Principle in the counts of radio galaxies at different frequencies
• The Atacama Cosmology Telescope: Cross-Correlation of CMB Lensing and Quasars
• Maximum a posteriori CMB lensing reconstruction
• Homogeneity and isotropy in the 2MASS Photometric Redshift catalogue
• Constraining Gravity at the Largest Scales through CMB Lensing and Galaxy Velocities
• Cross-correlating Planck CMB lensing with SDSS: Lensing-lensing and galaxy-lensing cross-correlations
• Exploring cosmic homogeneity with the BOSS DR12 galaxy sample
• Sparse component separation for accurate CMB map estimation
• Weak Lensing Detection in CMB Maps
• Gravitational Magnification of the Cosmic Microwave Background
• CMB Lensing Reconstruction in Real Space
• Statistical Isotropy of CMB Polarization Maps
• The dipole anisotropy of AllWISE galaxies
• Unveiling Hidden Patterns in CMB Anisotropy Maps
• Search for anomalous alignments of structures in Planck data using Minkowski Tensors
• Tensor Minkowski Functionals: first application to the CMB
• Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?
• Isotropy analyses of the Planck convergence map
• Tensor Minkowski Functionals for random fields on the sphere
• Testing isotropy in the Universe using photometric and spectroscopic data from the SDSS
• Probing statistical isotropy of cosmological radio sources using SKA
• Litmus Test for Cosmic Hemispherical Asymmetry in the Cosmic Microwave Background B-mode polarization
• The dipole anisotropy of WISE x SuperCOSMOS number counts
• Morphology of CMB fields -- effect of weak gravitational lensing
• Statistical Isotropy of the CMB E-mode signal

Cited by in corpus (4)

• Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?
• Excess of lensing amplitude in the Planck CMB power spectrum
• Minkowski Tensors in Redshift Space -- Beyond the Plane Parallel Approximation
• The geometrical meaning of statistical isotropy of smooth random fields in two dimensions