Statistics of phase correlations as a test for non-Gaussianity of the CMB maps

Abstract

Gaussianity is the very base for derivation of the cosmological parameters from the CMB angular power spectrum. Non-Gaussian signal, whether originated from experimental error or primordial source, could mimic extra power in the power spectrum, thereby leading to a wrong set of parameters. In this paper we present a new Gaussianity analysis of the derived CMB singals. It is based on the trigonometric moments of phases, which can be concluded with a ``mean angle'', allowing us to see the global trend of non-Gaussianity of the signals. These moments are also closely related to the Pearson's random walks. We apply these analyses on the derived CMB maps and their different morphologies manifest themselves through these functions. We also comment on rotational invariance of the trigonometric moments of phases as a non-Gaussianity test.

arXiv comment12 pages, submitted to PRD, more references added

References in corpus (31)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Non-Gaussianity from Inflation: Theory and Observations
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• Asymmetries in the CMB anisotropy field
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity
• A high resolution foreground cleaned CMB map from WMAP
• The Microwave Anisotropy Probe (MAP) Mission
• Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets
• Is the low-l microwave background cosmic?
• On Foreground Removal from the Wilkinson Microwave Anisotropy Probe Data by an Internal Linear Combination Method: Limitations and Implications
• Non-Gaussian Signatures in the Temperature Fluctuation Observed by the Wilkinson Microwave Anisotropy Probe
• Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing Methods and Systematic Errors Limits
• Non-Gaussianity of the derived maps from the first-year WMAP data
• Evidence for non-Gaussianity in the COBE DMR Four Year Sky Maps
• Gauss--Legendre Sky Pixelization (GLESP) for CMB maps
• The Hot and Cold Spots in the WMAP Data are Not Hot and Cold Enough
• Phase Correlations in Cosmic Microwave Background Temperature Maps
• A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map
• Constraints on mode couplings and modulation of the CMB with WMAP data
• On the Non-Gaussianity Observed in the COBE-DMR Sky Maps
• Phase Information and the Evolution of Cosmological Density Perturbations
• Primordial magnetic field and non-Gaussianity of the 1-year Wilkinson Microwave Anisotropy Probe (WMAP) data
• Phase cross-correlation of the WMAP ILC map and foregrounds
• Return mapping of phases and the analysis of the gravitational clustering hierarchy
• Looking for Cosmological Alfven Waves in WMAP Data
• Phase Mapping as a Powerful Diagnostic of Primordial Non-Gaussianity
• Cross-correlation of the CMB and foregrounds phases derived from the WMAP data
• Non-Random Phases in Non-Trivial Topologies
• Faraday Rotation as a Diagnostic of Galactic Foreground Contamination of CMB Maps

Cited by in corpus (28)

• On the large-angle anomalies of the microwave sky
• The Uncorrelated Universe: Statistical Anisotropy and the Vanishing Angular Correlation Function in WMAP Years 1-3
• Testing Gaussian random hypothesis with the cosmic microwave background temperature anisotropies in the three-year WMAP data
• Possible extensions of the standard cosmological model: anisotropy, rotation, and magnetic field
• A Scaling Index Analysis of the WMAP three year data: Signatures of non-Gaussianities and Asymmetries in the CMB
• Non-Gaussianity analysis on local morphological measures of WMAP data
• Pearson's random walk in the space of the CMB phases: evidence for parity asymmetry
• Random-Walk Statistics and the Spherical Harmonic Representation of CMB Maps
• Measuring the Three Point Correlation Function of the Cosmic Microwave Background
• Searching for non-Gaussianity in the WMAP data
• Scale dependent non-Gaussianities in the CMB data identified with Minkowski Functionals and Scaling Indices
• Is the cold spot responsible for the CMB North-South asymmetry?
• Polarized wavelets and curvelets on the sphere
• The One-dimensional Fourier Representation and Large Angular Scale Foreground Contamination in the 3-year Wilkinson Microwave Anisotropy Probe data
• Symmetry and anti-symmetry of the CMB anisotropy pattern
• Hemispherical power asymmetry: parameter estimation from CMB WMAP5 data
• Scale-dependent non-Gaussianities in the WMAP data as identified by using surrogates and scaling indices
• Real space tests of the statistical isotropy and Gaussianity of the WMAP CMB data
• Phase analysis of the cosmic microwave background from an incomplete sky coverage
• Probing non-Gaussianities in the CMB on an incomplete sky using surrogates
• Statistics of the excursion sets in models with local primordial non-Gaussianity
• Search for non-Gaussianities in the WMAP data with the Scaling Index Method
• Cross-Power Spectrum and Its Application on Window Functions in the WMAP data
• Anomalous frequency shifts in the solar system
• Phase statistics of the WMAP 7 year data
• Structure in Galaxy Distribution. III. Fourier Transforming the Universe
• Cosmic Microwave Background anisotropies: the power spectrum and beyond
• Investigating non-Gaussianity in Cosmic Microwave Background Temperature Maps using Spherical Harmonic Phases