P. Naselsky

Non-Gaussianity of the Derived Maps from the First-Year Wilkinson Microwave Anisotropy Probe Data

We present non-Gaussianity testing on recently-released derived maps from the first-year WMAP data by Tegmark, de Oliveria-Costa and Hamilton. Our test is based on a phase mapping technique which has the advantage of testing non-Gaussianity at separate multipole bands. We show that their foreground-cleaned map is against the random-phase hypothesis at all 4 multipole bands centered around l = 150, 290, 400 and 500. Their Wiener-filtered map, on the other hand, is Gaussian for l 350 as we detect certain degrees of phase coupling, hence against the random-phase hypothesis. Our phase mapping technique is particularly useful for testing the accuracy of component separation methods.We present non-Gaussianity testing on derived maps from the recently released first-year Wilkinson Microwave Anisotropy Probe data by Tegmark, de Oliveria-Costa, & Hamilton. Our test is based on a phase-mapping technique that has the advantage of testing non-Gaussianity at separate multipole bands. We show that their foreground-cleaned map is against the random-phase hypothesis at all four multipole bands centered around l = 150, 290, 400, and 500. Their Wiener-filtered map, on the other hand, is Gaussian for l 350 as we detect certain degrees of phase coupling, hence against the random-phase hypothesis. Our phase-mapping technique is particularly useful for testing the accuracy of component separation methods.

ANOMALOUS PARITY ASYMMETRY OF THE WILKINSON MICROWAVE ANISOTROPY PROBE POWER SPECTRUM DATA AT LOW MULTIPOLES

We have investigated non-Gaussianity of our early universe by comparing the parity asymmetry of the Wilkinson Microwave Anisotropy Probe (WMAP) power spectrum with simulations. We find that odd-parity preference of the WMAP data (2 ≤ l ≤ 18) is anomalous at 4-in-1000 level. We find it likely that low quadrupole power is part of this parity asymmetry rather than an isolated anomaly. Further investigation is required to find out whether the origin of this anomaly is a cosmological or a systematic effect. The data from Planck Surveyor, which has systematics distinct from WMAP, will help us to resolve the origin of the anomalous odd-parity preference.

Anomalous parity asymmetry of WMAP 7-year power spectrum data at low multipoles: Is it cosmological or systematics?

It is natural to assume a parity-neutral Universe and accordingly no particular parity preference in the cosmic microwave background sky. However, our investigation based on the WMAP 7-year power spectrum shows there exists a large-scale odd-parity preference with high statistical significance. We also find that the odd-parity preference in WMAP7 data is slightly higher than earlier releases. We have investigated possible origins, and ruled out various noncosmological origins. We also find that the primordial origin requires |Re[{Phi}(k)]|<<|Im[{Phi}(k)]| for k < or approx. 22/{eta}{sub 0}, where {eta}{sub 0} is the present conformal time. In other words, it requires translational invariance in the primordial Universe to be violated on scales larger than 4 Gpc. The Planck surveyor, which possesses wide frequency coverage and systematics distinct from the WMAP, may allow us to resolve the mystery of the anomalous odd-parity preference. Furthermore, polarization maps of large-sky coverage will reduce degeneracy in cosmological origins.

Primordial Magnetic Field and Non-Gaussianity of the One-Year Wilkinson Microwave Anisotropy Probe Data

Alfven turbulence caused by statistically isotropic and homogeneous primordial magnetic field induces correlations in the cosmic microwave background (CMB) anisotropies. The correlations are specifically between the spherical harmonic modes al-1,m and al+1,m. In this paper we approach this issue from phase analysis of the CMB maps derived from the WMAP data sets. Using circular statistics and return phase mapping, we examine phase correlation of Δl = 2 for the primordial non-Gaussianity caused by the Alfven turbulence at the epoch of recombination. Our analyses show that such specific features from the power-law Alfven turbulence do not contribute significantly in the phases of the maps and could not be a source of primordial non-Gaussianity of the CMB.

Phase Cross-Correlation of the Wilkinson Microwave Anisotropy Probe Internal Linear Combination Map and Foregrounds

We present a circular cross-correlation test for the phases of the Internal Linear Combination (ILC) map and the Wilkinson Microwave Anisotropy Probe foregrounds for all K-W frequency bands at the range of multipoles l ≤ 50. We have found significant deviations from the expected Poissonian statistics for the ILC and foreground phases. Our analysis shows that the low multipole range of the ILC power spectrum contains some residue of the foregrounds.We present a circular cross-correlation tests for the phases of the Internal Linear Combination Map (ILC) and WMAP’s foregrounds for all K–W frequency bands at the range of multipoles l ≤ 50. We have found significant deviations from the expected Poissonian statistics for the ILC and the foregrounds phases. Our analysis shows that the low multipole range of the ILC power spectrum contains some of the foregrounds residues. Subject headings: cosmology: cosmic microwave background — cosmology: observations — methods: data analysis

The Gauss-Legendre Sky Pixelization for the CMB polarization (GLESP-pol). Errors due to pixelization of the CMB sky

We present the development of the method for numerical analysis of polarization in the Gauss–Legendre sky pixelization (GLESP) scheme for CMB maps. This incorporation of the polarization transforms in the pixelization scheme GLESP completes the creation of our new method for numerical analysis of CMB maps. A comparison of GLESP and HEALPix calculations is done.

Cross-correlation of the phases of the CMB and foregrounds derived from the WMAP data

We present circular and linear cross-correlation tests and the ‘friend-of-friend’ analysis for phases of the Internal Linear Combination Map (ILC) and the WMAP foregrounds for all K−W frequency bands at the range of multipoles l≤ 100. We also compare Tegmark, de Oliveira-Costa & Hamilton and Naselsky et al. cleaned maps with corresponding foregrounds. We have found significant deviations from the expected Poissonian statistics for all the cleaned maps and foregrounds. Our analysis shows that, for a low multipole range of the cleaned maps, power spectra contain some of the foregrounds residuals mainly from the W band.

Departure from Gaussianity of the Cosmic Microwave Background Temperature Anisotropies in the Three-Year WMAP Data

We test the hypothesis that the temperature of the cosmic microwave background is consistent with a Gaussian random field defined on the celestial sphere, using the full sky debiased internal linear combination (DILC) map produced from the three-year WMAP data. We test the phases for spherical harmonic modes with l ≤ 10 (which should be the cleanest) for uniformity, randomness, and correlation with phases of the foreground maps. The phases themselves are consistent with a uniform distribution, but the differences between phases (randomness) are not consistent with uniformity. For l = 3 and l = 6, the phases of the CMB maps cross-correlate with the foregrounds, suggesting the presence of residual contamination in the DILC map even on these large scales. We also use a one-dimensional Fourier representation to assemble alm into the ΔTl() for each l mode and test the positions of the resulting maxima and minima for consistency with uniformity randomness on the unit circle. The results show significant departures at the 0.5% level, with the one-dimensional peaks concentrated around = 180°. This strongly significant alignment with the Galactic meridian, together with the cross-correlation of DILC phases with the foreground maps, strongly suggests that even the lowest spherical harmonic modes in the map are significantly contaminated with foreground radiation.

The Robustness of Phase Mapping as a Non-Gaussianity Test

The identification and extraction of non-Gaussian signals are two of the main cosmological challenges facing future experimental measurements of the cosmic microwave background temperature pattern. In this Letter we present a detailed account and test the robustness of a generalized statistical measure based on a novel method of representation of Fourier phases using the return map. We demonstrate the usefulness (and limitations) of this method by testing it on controlled simulated maps, which show that it is both robust and powerful, particularly in detecting non-Gaussianity from systematics.The identification and extraction of non-Gaussian signals is one of the main cosmological challenges facing future experimental measurements of the cosmic microwave background temperature pattern. We present a generalized statistical measure based on a novel technique representation of Fourier phases using the return map. We show that this method is both robust and powerful in comparison, for example, with morphological measures.

Understanding the WMAP Cold Spot mystery

The Cold Spot (CS) at galactic coordinates (b = −57°, l = 209°) was discovered in the Wilkinson Microwave Anisotropy Probe (WMAP)data as a cosmic background anomaly. In order to assess the cosmological significance of the Spot, we examine its properties using the cluster analysis of the local extrema in the cosmic microwave background (CMB) signal. We also check the hypothesis that the CMB signal has a non-Gaussian tail, localized in the low-multipole components. We constructed a linear filter, dividing the signal into two parts: non-Gaussian and Gaussian. Using the filter scale as a variable, we can maximize the skewness and kurtosis of the smoothed signal and minimize these statistics. We discovered that the shape of the CS is formed primarily by the components of the CMB signal represented by the multipoles between 10 ≤ ℓ ≤ 20, with a corresponding angular scale of about 5°–10°. This signal leads to the modulation of the CMB on the whole sky, clearly seen at |b| > 30° in both the ILC andWCM maps, rather than in a single localized feature. After subtraction of this modulation, the remaining part of the CMB signal appears to be consistent with statistical homogeneity and Gaussianity. We therefore infer that the mystery of the WMAP Cold Spot reflects directly the peculiarities of low multipoles of the CMB signal, rather than a single local (isolated) defect or the manifestations of a globally anisotropic cosmology.