[Paper Review] Non-Gaussianity detections in the Bianchi VIIh corrected WMAP 1-year data made with directional spherical wavelets

Jason D. McEwen, M. P. Hobson+2 more|arXiv (Cornell University)|Oct 12, 2005

Geophysics and Gravity Measurements4 citations

TL;DR

This study investigates whether non-Gaussianity detections in WMAP 1-year CMB data—previously identified using directional spherical wavelets—persist after correcting for a best-fit Bianchi VIIh component. While kurtosis-based non-Gaussianity signals vanish due to suppression of the cold spot at (l,b) = (209°,−57°), skewness-based detections remain significant at 98.4%, indicating cosmological non-Gaussianity beyond the Bianchi model, with no evidence linking the signal to foregrounds or systematics.

ABSTRACT

Many of the current anomalies reported in the Wilkinson Microwave Anisotropy Probe (WMAP) 1-year data disappear after `correcting' for the best-fit embedded Bianchi type VII_h component (Jaffe et al. 2005), albeit assuming no dark energy component. We investigate the effect of this Bianchi correction on the detections of non-Gaussianity in the WMAP data that we previously made using directional spherical wavelets (McEwen et al. 2005a). As previously discovered by Jaffe et al. (2005), the deviations from Gaussianity in the kurtosis of spherical Mexican hat wavelet coefficients are eliminated once the data is corrected for the Bianchi component. This is due to the reduction of the cold spot at Galactic coordinates (l,b)=(209^\circ,-57\circ), which Cruz et al. (2005) claim to be the source of non-Gaussianity introduced in the kurtosis. Our previous detections of non-Gaussianity observed in the skewness of spherical wavelet coefficients are not reduced by the Bianchi correction. Indeed, the most significant detection of non-Gaussianity made with the spherical real Morlet wavelet at a significant level of 98.4% remains (using a very conservative method to estimate the significance). We make our code to simulate Bianchi induced temperature fluctuations publicly available.

Motivation & Objective

• To assess whether non-Gaussianity detections in WMAP 1-year CMB data, previously found using directional spherical wavelets, are affected by correction for a Bianchi VIIh component.
• To determine whether the Bianchi correction eliminates non-Gaussianity signals, particularly those linked to the cold spot at (l,b) = (209°,−57°).
• To evaluate whether residual non-Gaussianity in the corrected data is due to foreground contamination or instrumental systematics.
• To investigate the robustness of non-Gaussianity detections in skewness and kurtosis of wavelet coefficients after removing the Bianchi template.
• To provide publicly available code for simulating Bianchi-induced temperature fluctuations in CMB data.

Proposed method

• Applied the best-fit Bianchi VIIh template from Jaffe et al. (2005) to correct the WMAP internal linear combination (ILC) map, using updated shear and vorticity estimates.
• Re-analyzed the Bianchi-corrected data using directional spherical wavelets, specifically the spherical Mexican hat and real Morlet wavelets, to compute skewness and kurtosis of wavelet coefficients.
• Employed a conservative significance estimation method for wavelet-based non-Gaussianity detection, calculating p-values via Monte Carlo simulations.
• Conducted χ² tests combining multiple wavelet statistics to assess overall deviation from Gaussianity in the corrected data.
• Localized regions contributing most strongly to non-Gaussianity detections using wavelet coefficient maps and compared these across original and corrected data.
• Performed preliminary tests to rule out foregrounds and systematics as the source of the remaining non-Gaussian signal.

Experimental results

Research questions

• RQ1 Does correcting the WMAP 1-year data for the best-fit Bianchi VIIh component eliminate non-Gaussianity detections previously found using directional spherical wavelets?
• RQ2 To what extent does the cold spot at (l,b) = (209°,−57°) contribute to kurtosis-based non-Gaussianity in the wavelet analysis?
• RQ3 Are the remaining non-Gaussianity detections in the skewness of wavelet coefficients affected by the Bianchi correction?
• RQ4 Could the persistent non-Gaussian signal in the corrected data be attributed to residual foreground contamination or instrumental systematics?
• RQ5 What is the significance of the remaining non-Gaussianity in the context of cosmological models beyond the standard Gaussian, isotropic framework?

Key findings

• The kurtosis-based non-Gaussianity detections in the spherical Mexican hat wavelet coefficients vanish after correcting for the Bianchi VIIh component, consistent with prior findings by Jaffe et al. (2005).
• The cold spot at Galactic coordinates (l,b) = (209°,−57°) is significantly reduced in magnitude and size following the Bianchi correction, explaining the elimination of kurtosis-based non-Gaussianity.
• The skewness-based non-Gaussianity detection in the real Morlet wavelet coefficients remains highly significant at 98.4% in the Bianchi-corrected data, using a conservative significance estimation method.
• The χ² test across all wavelet statistics confirms that the Bianchi-corrected data still deviates significantly from Gaussianity, primarily due to the persistent skewness signal.
• The regions identified as the main contributors to non-Gaussianity in the corrected data are largely unchanged from those found in the original data, indicating the signal's robustness to the Bianchi correction.
• Preliminary analysis rules out foreground contamination and systematics as the source of the remaining non-Gaussian signal, suggesting a cosmological origin.