arXiv subjects

J. D. McEwen

Publications and source records attributed to J. D. McEwen.

66 records · Page 4Linked to original sources

arXiv2007

Bianchi VII_h models and the cold spot texture

We have returned to our previous Bianchi VII_h analysis in light of the Cruz et al. 2007 suggestion that the cold spot observed near the southern Galactic pole may be a remnant temperature perturbation of a cosmic texture. In Bridges et al. 2006b we found two favoured left handed Bianchi VII_h templates with restricted prior probabilities so that the template was centred close to the cold spot. Using WMAP data `corrected' for the texture fit we have now reexamined both models to assess any changes to these conclusions. We find that both models are left almost entirely unconstrained by the data and consequently exhibit significantly reduced Bayesian evidences. Both models are now disfavoured by the data. This result reinforces our previous suggestion that the cold spot was likely to be driving any Bianchi VII_h detection.

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arXiv2007

Markov chain Monte Carlo analysis of Bianchi VII_h models

We have extended the analysis of Jaffe et al. to a complete Markov chain Monte Carlo (MCMC) study of the Bianchi type ${\rm VII_h}$ models including a dark energy density, using 1-year and 3-year Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background (CMB) data. Since we perform the analysis in a Bayesian framework our entire inference is contained in the multidimensional posterior distribution from which we can extract marginalised parameter constraints and the comparative Bayesian evidence. Treating the left-handed Bianchi CMB anisotropy as a template centred upon the `cold-spot' in the southern hemisphere, the parameter estimates derived for the total energy density, `tightness' and vorticity from 3-year data are found to be: $Ω_{tot} = 0.43\pm 0.04$, $h = 0.32^{+0.02}_{-0.13}$, $ω= 9.7^{+1.6}_{-1.5}\times 10^{-10}$ with orientation $γ= {337^{\circ}}^{+17}_{-23}$). This template is preferred by a factor of roughly unity in log-evidence over a concordance cosmology alone. A Bianchi type template is supported by the data only if its position on the sky is heavily restricted. The low total energy density of the preferred template, implies a geometry that is incompatible with cosmologies inferred from recent CMB observations. Jaffe et al. found that extending the Bianchi model to include a term in $Ω_Λ$ creates a degeneracy in the $Ω_m - Ω_Λ$ plane. We explore this region fully by MCMC and find that the degenerate likelihood contours do not intersect areas of parameter space that 1 or 3 year WMAP data would prefer at any significance above $2σ$. Thus we can confirm that a physical Bianchi ${\rm VII_h}$ model is not responsible for this signature.

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arXiv2007

Detecting dark energy with wavelets on the sphere

Dark energy dominates the energy density of our Universe, yet we know very little about its nature and origin. Although strong evidence in support of dark energy is provided by the cosmic microwave background, the relic radiation of the Big Bang, in conjunction with either observations of supernovae or of the large scale structure of the Universe, the verification of dark energy by independent physical phenomena is of considerable interest. We review works that, through a wavelet analysis on the sphere, independently verify the existence of dark energy by detecting the integrated Sachs-Wolfe effect. The effectiveness of a wavelet analysis on the sphere is demonstrated by the highly statistically significant detections of dark energy that are made. Moreover, the detection is used to constrain properties of dark energy. A coherent picture of dark energy is obtained, adding further support to the now well established cosmological concordance model that describes our Universe.

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arXiv2007

Complex data processing: fast wavelet analysis on the sphere

In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the plane and on the sphere. Two fast algorithms are also presented for the analysis of signals on the sphere with steerable wavelets.

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arXiv2007

Cosmological applications of a wavelet analysis on the sphere

The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerful techniques available to cosmologists for placing strong constraints on the cosmological parameters that describe the origin, content and evolution of the Universe. The last decade has witnessed the introduction of wavelet analyses in cosmology and, in particular, their application to the CMB. We review here spherical wavelet analyses of the CMB that test the standard cosmological concordance model. The assumption that the temperature anisotropies of the CMB are a realisation of a statistically isotropic Gaussian random field on the sphere is questioned. Deviations from both statistical isotropy and Gaussianity are detected in the reviewed works, suggesting more exotic cosmological models may be required to explain our Universe. We also review spherical wavelet analyses that independently provide evidence for dark energy, an exotic component of our Universe of which we know very little currently. The effectiveness of accounting correctly for the geometry of the sphere in the wavelet analysis of full-sky CMB data is demonstrated by the highly significant detections of physical processes and effects that are made in these reviewed works.

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arXiv2007

Detection of the ISW effect and corresponding dark energy constraints made with directional spherical wavelets

Using a directional spherical wavelet analysis we detect the integrated Sachs-Wolfe (ISW) effect, indicated by a positive correlation between the first-year Wilkinson Microwave Anisotropy Probe (WMAP) and NRAO VLA Sky Survey (NVSS) data. Detections are made using both a directional extension of the spherical Mexican hat wavelet and the spherical butterfly wavelet. We examine the possibility of foreground contamination and systematics in the WMAP data and conclude that these factors are not responsible for the signal that we detect. The wavelet analysis inherently enables us to localise on the sky those regions that contribute most strongly to the correlation. On removing these localised regions the correlation that we detect is reduced in significance, as expected, but it is not eliminated, suggesting that these regions are not the sole source of correlation between the data. This finding is consistent with predictions made using the ISW effect, where one would expect weak correlations over the entire sky. In a flat universe the detection of the ISW effect provides direct and independent evidence for dark energy. We use our detection to constrain dark energy parameters by deriving a theoretical prediction for the directional wavelet covariance statistic for a given cosmological model. Comparing these predictions with the data we place constraints on the equation-of-state parameter $w$ and the vacuum energy density $Ω_Λ$. We also consider the case of a pure cosmological constant, i.e. $w=-1$. For this case we rule out a zero cosmological constant at greater than the 99.9% significance level. All parameter estimates that we obtain are consistent with the standand cosmological concordance model values.

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arXiv2006

A high-significance detection of non-Gaussianity in the WMAP 3-year data using directional spherical wavelets

We repeat the directional spherical real Morlet wavelet analysis used to detect non-Gaussianity in the WMAP 1-year data (McEwen et al. 2005a), on the WMAP 3-year data. The non-Gaussian signal previously detected is indeed present in the 3-year data, although the significance of the detection is reduced. Using our most conservative method for constructing significance measures, we find the significance of the detection of non-Gaussianity drops from 98.3+/-0.4% to 94.9+/-0.7%; the significance drops from 99.3+/-0.3% to 97.2+/-0.5% using a method based on the $χ^2$ statistic. The wavelet analysis allows us to localise most likely sources of non-Gaussianity on the sky. We detect very similar localised regions in the WMAP 1-year and 3-year data, although the regions extracted appear more pronounced in the 3-year data. When all localised regions are excluded from the analysis the 3-year data is consistent with Gaussianity.

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arXiv2006

A directional continuous wavelet transform on the sphere

A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more general directional framework. Directional wavelets are a powerful extension that allow one to also probe oriented structure in the analysed function. Our spherical wavelet methodology has the advantage that all functions and operators are defined directly on the sphere. The construction of wavelets in our framework is demonstrated with an example.

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arXiv2006

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

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.

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arXiv2006

Fast directional continuous spherical wavelet transform algorithms

We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al. Fast algorithms for performing the directional continuous wavelet analysis on the unit sphere are presented. The fast directional algorithm, based on the fast spherical convolution algorithm developed by Wandelt and Gorski, provides a saving of O(sqrt(Npix)) over a direct quadrature implementation for Npix pixels on the sphere, and allows one to perform a directional spherical wavelet analysis of a 10^6 pixel map on a personal computer.

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arXiv2005

A high-significance detection of non-Gaussianity in the WMAP 1-year data using directional spherical wavelets

A directional spherical wavelet analysis is performed to examine the Gaussianity of the WMAP 1-year data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows one to probe orientated structure in the data. Significant deviations from Gaussianity are detected in the skewness and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet coefficients for both the WMAP and Tegmark et al. (2003) foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. (2003) using the spherical symmetric Mexican hat wavelet is confirmed, although their detection at the 99.9% significance level is only made at the 95.3% significance level using our most conservative statistical test. Furthermore, deviations from Gaussianity in the skewness of spherical real Morlet wavelet coefficients on a wavelet scale of 550 arcmin (corresponding to an effective global size on the sky of approximately 26 degrees and an internal size of 3 degrees) at an azimuthal orientation of 72 degrees, are made at the 98.3% significance level, using the same conservative method. The wavelet analysis inherently allows one to localise on the sky those regions that introduce skewness and those that introduce kurtosis. Preliminary noise analysis indicates that these detected deviation regions are not atypical and have average noise dispersion. Further analysis is required to ascertain whether these detected regions correspond to secondary or instrumental effects, or whether in fact the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave background.

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arXiv2004

A fast directional continuous spherical wavelet transform

A fast algorithm for Antoine and Vandergheynst's (1998) directional continuous spherical wavelet transform (CSWT) is presented. Computational requirements are reduced by a factor of O(\sqrt{N}), when N is the number of pixels on the sphere. The spherical Mexican hat wavelet Gaussianity analysis of the WMAP 1-year data performed by Vielva et al. (2003) is reproduced and confirmed using the fast CSWT. The proposed extension to directional analysis is inherently afforded by the fast CSWT algorithm.

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